Perspectives on geometric analysis

This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical Society. I dedicate the lecture to the memory of my teacher S.S. Chern who had passed away in December 2004.

[1]  Michael T. Anderson.  The Dirichlet problem at infinity for manifolds of negative curvature , 1983 .

[2]  R. Borcherds.  Automorphic forms onOs+2,2(R) and infinite products , 1995 .

[3]  Thomas H. Parker,et al.  Pseudo-holomorphic maps and bubble trees , 1993 .

[4]  Mirror symmetry is T duality , 1996, hep-th/9606040.

[5]  Shing-Tung Yau,et al.  A GENERAL SCHWARZ LEMMA FOR KAHLER MANIFOLDS. , 1978 .

[6]  D. Gieseker.  On the moduli of vector bundles on an algebraic surface , 1977 .

[7]  P. Griffiths,et al.  Locally homogeneous complex manifolds , 1969 .

[8]  H. Lawson,et al.  On boundaries of complex analytic varieties, II , 1975 .

[9]  Y. Siu.  Every K3 surface is Kähler , 1983 .

[10]  Martin points on open manifolds of non-positive curvature , 2005, math/0505575.

[11]  P. Sarnak,et al.  $L^\infty$ norms of eigenfunctions of arithmetic surfaces , 1995 .

[12]  Enrico Giusti,et al.  The singular set of the minima of certain quadratic functionals , 1984 .

[13]  A. O. Houcine.  On hyperbolic groups , 2006 .

[14]  Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman , 2003, math/0308090.

[15]  S. Yau,et al.  On the structure of manifolds with positive scalar curvature , 1979 .

[16]  N. Leung.  Topological quantum field theory for Calabi-Yau threefolds and G-2 manifolds , 2002, math/0208124.

[17]  Duality and Fibrations on G_2 Manifolds , 2002, hep-th/0203217.

[18]  E. Calabi,et al.  Sur les variétés complexes compactes localement symétriques , 1959 .

[19]  Regularizing a Singular Special Lagrangian Variety , 2001, math/0110053.

[20]  Xiaowei Wang.  Balance point and Stability of Vector Bundles Over a Projective Manifold , 2002 .

[21]  P. Gauduchon.  La 1-forme de torsion d'une variété hermitienne compacte , 1984 .

[22]  Gerhard Huisken,et al.  Mean curvature flow singularities for mean convex surfaces , 1999 .

[23]  Victor V. Batyrev,et al.  Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties , 1993, alg-geom/9310003.

[24]  S. Yau,et al.  Proof of the positive mass theorem. II , 1981 .

[25]  Jun Li.  The Geometry of Moduli Spaces of Vector Bundles over Algebraic Surfaces , 1995 .

[26]  Shlomo Sternberg,et al.  Convexity properties of the moment mapping. II , 1982 .

[27]  R. Bott,et al.  THE STABLE HOMOTOPY OF THE CLASSICAL GROUPS. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Terence Tao,et al.  Low-regularity global solutions to nonlinear dispersive equations , 2002 .

[29]  Zhiqin Lu.  On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch , 2000 .

[30]  D. Mcduff.  Examples of symplectic structures , 1987 .

[31]  C. Vafa.  Topological Mirrors and Quantum Rings , 1991 .

[32]  Xu-jia Wang,et al.  Kahler-Ricci solitons on toric manifolds with positive first Chern class , 2004 .

[33]  Paul Yang,et al.  An a priori estimate for a fully nonlinear equation on four-manifolds , 2002 .

[34]  Nicholas J. Korevaar.  Upper bounds for eigenvalues of conformal metrics , 1993 .

[35]  F. Ledrappier,et al.  The Poisson boundary for rank one manifolds and their cocompact lattices , 1994 .

[36]  Complex-analyticity of harmonic maps and strong rigidity of compact Kähler manifolds. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[37]  Changshou Lin.  The local isometric embedding in $\mathbf{R}^3$ of 2-dimensional Riemannian manifolds with nonnegative curvature , 1985 .

[38]  G. Rassias.  Algebraic and differential topology--global differential geometry , 1984 .

[39]  Claus Gerhardt.  H-surfaces in Lorentzian manifolds , 1983 .

[40]  M. Stern.  L2-index theorems on locally symmetric spaces , 1989 .

[41]  C. Böhm.  Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces , 1998 .

[42]  U. Pinkall,et al.  Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras , 1993 .

[43]  G. Huisken,et al.  The inverse mean curvature flow and the Riemannian Penrose Inequality , 2001 .

[44]  Shing-Tung Yau,et al.  The existence of negatively Ricci curved metrics on three manifolds , 1986 .

[45]  Nicholas P. Warner,et al.  Chiral rings in N = 2 superconformal theories , 1989 .

[46]  R. Hamilton.  Three-manifolds with positive Ricci curvature , 1982 .

[47]  D. Mcduff.  The structure of rational and ruled symplectic 4-manifolds , 1990 .

[48]  G. A. Margulis,et al.  Explicit constructions of graphs without short cycles and low density codes , 1982, Comb..

[49]  Matthias Günthier,et al.  On the perturbation problem associated to isometric embeddings of Riemannian manifolds , 1989 .

[50]  K. Kodaira,et al.  On a Differential-Geometric Method in the Theory of Analytic Stacks. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Locally Non-isometric yet Super Isospectral Spaces , 1999 .

[52]  Richard Schoen,et al.  The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature , 1980 .

[53]  K. Corlette.  Archimedean superrigidity and hyperbolic geometry , 1992 .

[54]  M. Schmidt.  A proof of the Willmore conjecture , 2002, math/0203224.

[55]  N. Hitchin.  The moduli space of special Lagrangian submanifolds , 1997, dg-ga/9711002.

[56]  V. Guillemin,et al.  Some inverse spectral results for negatively curved 2-manifolds , 1980 .

[57]  S. Yau,et al.  Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature , 1982 .

[58]  On the Cohomology of Locally Symmetric Spaces and of their Compactifications , 2003, math/0306403.

[59]  Shing-Tung Yau,et al.  On the Schrödinger equation and the eigenvalue problem , 1983 .

[60]  A. Floer,et al.  An instanton-invariant for 3-manifolds , 1988 .

[61]  Jongsu Kim,et al.  Scalar-flat Kähler surfaces of all genera. , 1994, dg-ga/9409002.

[62]  Finiteness of arithmetic Kleinian reflection groups , 2005, math/0512560.

[63]  E. Witten.  Elliptic genera and quantum field theory , 1987 .

[64]  H. Lawson,et al.  Calibrated geometries , 1982 .

[65]  L. Hörmander.  Fourier integral operators. I , 1995 .

[66]  S. Donaldson.  Lefschetz pencils on symplectic manifolds , 1999 .

[67]  Werner Müller,et al.  Analytic torsion and R-torsion of Riemannian manifolds , 1978 .

[68]  H. Lawson,et al.  On Stable Currents and Their Application to Global Problems in Real and Complex Geometry , 1973 .

[69]  J. Kaminker.  Geometric and Topological Invariants of Elliptic Operators , 1990 .

[70]  V. Guillemin,et al.  Eigenvalues associated with a closed geodesic , 1976 .

[71]  Nancy Hingston,et al.  On the growth of the number of closed geodesics on the two-sphere , 1993 .

[72]  S. Yau,et al.  On the regularity of the solution of the n‐dimensional Minkowski problem , 1976 .

[73]  R. Geroch,et al.  ENERGY EXTRACTION * , 1973 .

[74]  Mirror Principle I , 1997, alg-geom/9712011.

[75]  P. Newstead.  Moduli Spaces and Vector Bundles: Geometric Invariant Theory , 2009 .

[76]  M. Berger.  Sur quelques variétés d'Einstein compactes , 1961 .

[77]  T. Li,et al.  GENERAL WALL CROSSING FORMULA , 2004 .

[78]  G. Perelman.  Finite extinction time for the solutions to the Ricci flow on certain three-manifolds , 2003, math/0307245.

[79]  E. Witten.  Monopoles and four-manifolds , 1994, hep-th/9411102.

[80]  William K. Allard,et al.  On the First Variation of a Varifold: Boundary Behavior , 1975 .

[81]  W. Nahm.  On electric-magnetic duality , 1997 .

[82]  Heterotic Strings with Torsion , 2002, hep-th/0209077.

[83]  G. Uhlmann,et al.  The boundary distance function and the Dirichlet-to-Neumann map , 2004 .

[84]  J. Cheeger.  Analytic torsion and Reidemeister torsion. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[85]  M. Gross.  Special Lagrangian fibrations. I. Topology,” Integrable systems and algebraic geometry (Kobe/Kyoto , 1997 .

[86]  Twisted connected sums and special Riemannian holonomy , 2000, math/0012189.

[87]  Nicholas T. Varopoulos,et al.  Analysis and Geometry on Groups , 1993 .

[88]  Kefeng Liu.  HEAT KERNEL AND MODULI SPACES , 1996 .

[89]  J. Bismut,et al.  Equivariant de Rham torsions , 2004 .

[90]  P. Griffiths.  Complex-Analytic Properties of Certain Zariski Open Sets on Algebraic Varieties , 1971 .

[91]  D. joyce.  Compact 8-manifolds with holonomy Spin(7) , 1996 .

[92]  D. Catlin.  The Bergman Kernel and a Theorem of Tian , 1999 .

[93]  S. Yau,et al.  Upper bound for the first eigenvalue of algebraic submanifolds , 1994 .

[94]  Roan Shishyr,et al.  On Ricci flat 3-fold , 1987 .

[95]  D. joyce.  Compact Riemannian 7-manifolds with holonomy $G\sb 2$. II , 1996 .

[96]  Neshan Wickramasekera.  A Rigidity Theorem for Stable Minimal Hypercones , 2004 .

[97]  Braid group actions on derived categories of coherent sheaves , 2000, math/0001043.

[98]  S. Yau,et al.  Compact group actions and the topology of manifolds with non-positive curvature , 1979 .

[99]  R. Bott,et al.  On the rigidity theorems of Witten , 1989 .

[100]  D. Abramovich.  A linear lower bound on the gonality of modular curves , 1996, alg-geom/9609012.

[101]  Gauge theory and calibrated geometry, I , 2000 .

[102]  Jian-Shu Li.  KLOOSTERMAN-SELBERG ZETA FUNCTIONS ON COMPLEX HYPERBOLIC SPACES , 1991 .

[103]  Neshan Wickramasekera.  On the singularities and a Bernstein property of immersed stable minimal hypersurfaces , 2005 .

[104]  W. Thurston.  Three dimensional manifolds, Kleinian groups and hyperbolic geometry , 1982 .

[105]  S. Yau,et al.  Existence of black hole solutions for the Einstein-Yang/Mills equations , 1993 .

[106]  M. Goresky,et al.  INTERSECTION HOMOLOGY THEORY , 1980 .

[107]  J. H. Michael,et al.  Sobolev and mean‐value inequalities on generalized submanifolds of Rn , 1973 .

[108]  Andrejs E. Treibergs.  Entire spacelike hypersurfaces of constant mean curvature in Minkowski Space , 1980 .

[109]  S. Yau,et al.  The Poincaré-Lelong equation on complete Kähler manifolds , 1981 .

[110]  G. Huisken.  Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature , 1986 .

[111]  W. Barth,et al.  A decomposability criterion for algebraic 2-bundles on projective spaces , 1974 .

[112]  Michael Atiyah,et al.  The index of elliptic operators on compact manifolds , 1963 .

[113]  E. Witten.  A new proof of the positive energy theorem , 1981 .

[114]  Robert Gulliver,et al.  Regularity of Minimizing Surfaces of Prescribed Mean Curvature , 1973 .

[115]  John Franks,et al.  Geodesics onS2 and periodic points of annulus homeomorphisms , 1992 .

[116]  L. Saper,et al.  L(2)-cohomology of arithmetic varieties. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[117]  Wendell H. Fleming,et al.  Normal and Integral Currents , 1960 .

[118]  L. Hörmander,et al.  An introduction to complex analysis in several variables , 1973 .

[119]  S. Novikov,et al.  MULTIVALUED FUNCTIONS AND FUNCTIONALS. AN ANALOGUE OF THE MORSE THEORY , 2007 .

[120]  G. Talenti,et al.  Best constant in Sobolev inequality , 1976 .

[121]  S. Yau,et al.  Complete affine hypersurfaces. Part I. The completeness of affine metrics , 1986 .

[122]  M. Gromov.  Pseudo holomorphic curves in symplectic manifolds , 1985 .

[123]  M. Atiyah.  New invariants of 3 and 4 dimensional manifolds , 1987 .

[124]  Shing-Tung Yau,et al.  Existence of incompressible minimal surfaces and the topology of three - dimensional manifolds with , 1979 .

[125]  A. Chenciner.  A note by Poincare , 2005 .

[126]  G. Tian.  On Calabi's conjecture for complex surfaces with positive first Chern class , 1990 .

[127]  R. Schoen,et al.  Sobolev spaces and harmonic maps for metric space targets , 1993 .

[128]  Shing-Tung Yau,et al.  A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces , 1982 .

[129]  T. Colding.  Shape of manifolds with positive Ricci curvature , 1996 .

[130]  Shing-Tung Yau,et al.  Isoperimetric constants and the first eigenvalue of a compact riemannian manifold , 1975 .

[131]  Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature , 2005, math/0504478.

[132]  T. Aubin,et al.  Problèmes isopérimétriques et espaces de Sobolev , 1976 .

[133]  S. Yau.  A Note on the Distribution of Critical Points of Eigenfunctions , 1997 .

[134]  Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature , 2002, math/0301047.

[135]  T. Hoffmann-Ostenhof,et al.  Critical sets of smooth solutions to elliptic equations in dimension 3 , 1996 .

[136]  G. Perelman.  The entropy formula for the Ricci flow and its geometric applications , 2002, math/0211159.

[137]  E. Calabi.  On Kähler Manifolds with Vanishing Canonical Class , 1957 .

[138]  A study of the Hilbert-Mumford criterion for the stability of projective varieties , 2004, math/0412519.

[139]  A. Borel,et al.  Corners and arithmetic groups , 1973 .

[140]  Wan-Xiong Shi.  Ricci flow and the uniformization on complete noncompact Kähler manifolds , 1997 .

[141]  S. Yau,et al.  Harmonic maps and rigidity theorems for spaces of nonpositive curvature , 1999 .

[142]  C. Taubes.  Counting pseudo-holomorphic submanifolds in dimension 4 , 1996 .

[143]  H. Grauert,et al.  Hermitesche Metriken und normale Familien holomorpher Abbildungen , 1965 .

[144]  E. Witten.  Supersymmetry and Morse theory , 1982 .

[145]  B. Shiffman.  Complete characterization of holomorphic chains of codimension one , 1986 .

[146]  N. Nadirashvili,et al.  Eigenfunctions with few critical points , 1999 .

[147]  R. Ye.  Gromov’s compactness theorem for pseudo holomorphic curves , 1994 .

[148]  Peter Li.  Harmonic sections of polynomial growth , 1997 .

[149]  Y. Ruan,et al.  A mathematical theory of quantum cohomology , 1994 .

[150]  D. Mcduff.  Singularities and positivity of intersections of J-holomorphic curves , 1994 .

[151]  S. Yau,et al.  Compact manifolds of nonpositive curvature , 1972 .

[152]  Wolfgang Meyer,et al.  Periodic geodesics on compact riemannian manifolds , 1969 .

[153]  Karen K. Uhlenbeck.  Harmonic maps into Lie groups: classical solutions of the chiral model , 1989 .

[154]  Nancy Hingston,et al.  Equivariant Morse theory and closed geodesics , 1984 .

[155]  T. Colding,et al.  HARMONIC FUNCTIONS ON MANIFOLDS , 1997 .

[156]  E. Zehnder,et al.  Finite energy foliations of tight three-spheres and Hamiltonian dynamics , 2003 .

[157]  S. Osher.  A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations , 1993 .

[158]  Continuous families of isospectral Riemannian metrics which are not locally isometric , 1997, dg-ga/9702011.

[159]  A. Borel.  Some metric properties of arithmetic quotients of symmetric spaces , 1970 .

[160]  J. Bismut,et al.  Milnor and ray-singer metrics on the equivariant determinant of a flat vector bundle , 1994 .

[161]  R. Hamilton.  Four-manifolds with positive isotropic curvature , 1997 .

[162]  M. Gromov,et al.  Spin and Scalar Curvature in the Presence of a Fundamental Group. I , 1980 .

[163]  Takao Yamaguchi,et al.  Collapsing Three-Manifolds Under a Lower Curvature Bound , 2000 .

[164]  R. Hardt,et al.  Boundary regularity and embedded solutions for the oriented Plateau problem , 1979 .

[165]  S. Sternberg,et al.  Convexity properties of the moment mapping , 1982 .

[166]  Theorems on the Regularity and Singularity of Minimal Surfaces and Harmonic Maps , 1996 .

[167]  A spectral proof of Rademacher's conjecture for congruence subgroups of the modular group. , 1991 .

[168]  C. Terng.  A Higher Dimension Generalization of the Sine-Gordon Equation and its Soliton Theory , 1980 .

[169]  Chiu-Chu Melissa Liu,et al.  Positivity of quasi-local mass II , 2004, math/0412292.

[170]  C. McMullen.  Riemann surfaces and the geometrization of 3-manifolds , 1992, math/9210224.

[171]  F. Lin.  Nodal sets of solutions of elliptic and parabolic equations , 1991 .

[172]  N. Seiberg,et al.  Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory , 1994 .

[173]  E. Giusti,et al.  Harnack's inequality for elliptic differential equations on minimal surfaces , 1972 .

[174]  J. Nash.  C 1 Isometric Imbeddings , 1954 .

[175]  C. Callias.  Axial anomalies and index theorems on open spaces , 1978 .

[176]  N. J. Hitchin,et al.  Harmonic maps from a 2-torus to the 3-sphere , 1990 .

[177]  M. Atiyah.  Sir Michael Atiyah : a great mathematician of the twentieth century , 1999 .

[178]  J. Bismut,et al.  An extension of a theorem by Cheeger and Müller , 1992 .

[179]  On complete noncompact Kähler manifolds with positive bisectional curvature , 2002, math/0211370.

[180]  Salomon Bochner,et al.  Curvature and Betti numbers , 1948 .

[181]  A counterexample to the Hodge conjecture for Kaehler varieties , 2001, math/0112247.

[182]  M. Freedman,et al.  Least area incompressible surfaces in 3-manifolds , 1983 .

[183]  Y. Ruan.  Symplectic topology on algebraic 3-folds , 1994 .

[184]  R. Borcherds.  The moduli space of Enriques surfaces and the fake monster Lie superalgebra , 1996 .

[185]  R. Schoen,et al.  GEOMETRIC BOUNDS ON THE LOW EIGENVALUES OF A COMPACT SURFACE , 1980 .

[186]  R. Hamilton.  The Harnack estimate for the Ricci flow , 1993 .

[187]  M. Kuranishi.  Strongly Pseudoconvex CR structures over Small Balls: Part I. An a Priori Estimate , 1982 .

[188]  K. Kodaira.  On Kahler Varieties of Restricted Type An Intrinsic Characterization of Algebraic Varieties) , 1954 .

[189]  I. Ekeland,et al.  Symplectic topology and Hamiltonian dynamics , 1989 .

[190]  J. Jost,et al.  Mathematik in den Naturwissenschaften Leipzig Regularity Theorems and Energy Identities for Dirac-Harmonic Maps , 2004 .

[191]  M. Gromov.  Kähler hyperbolicity and $L_2$-Hodge theory , 1991 .

[192]  S. Yau,et al.  The existence of embedded minimal surfaces and the problem of uniqueness , 1982 .

[193]  Maxim Kontsevich,et al.  Feynman Diagrams and Low-Dimensional Topology , 1994 .

[194]  D. Christodoulou,et al.  On the regularity of spherically symmetric wave maps , 1993 .

[195]  Steve Zelditch,et al.  Spectral determination of analytic bi-axisymmetric plane domains , 2000 .

[196]  P. Sarnak.  Additive number theory and maass forms , 1984 .

[197]  C. Terng,et al.  MINIMAL HYPERSURFACES OF SPHERES WITH CONS TANT SCALAR CURVATURE , 1984 .

[198]  Helmut Friedrich,et al.  Hyperbolic reductions for Einstein's equations , 1996 .

[199]  L. Saloff-Coste,et al.  Analysis on Riemannian co-compact covers , 2004 .

[200]  Dennis Sullivan,et al.  Infinitesimal computations in topology , 1977 .

[201]  V. Mehta,et al.  Restriction of stable sheaves and representations of the fundamental group , 1984 .

[202]  A. Strominger.  Superstrings with Torsion , 1986 .

[203]  Uniqueness of the Ricci flow on complete noncompact manifolds , 2005, math/0505447.

[204]  N. Hitchin.  THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE , 1987 .

[205]  Sidney Frankel.  Complex geometry of convex domains that cover varieties , 1989 .

[206]  Jia-Xing Hong,et al.  Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature , 2003 .

[207]  L. Simon.  Existence of Willmore surfaces , 1986 .

[208]  T. Mabuchi.  K-ENERGY MAPS INTEGRATING FUTAKI INYARIANTS , 1986 .

[209]  S. Yau,et al.  Topology of three dimensional manifolds and the embedding problems in minimal surface theory , 1980 .

[210]  G. Mostow.  Strong Rigidity of Locally Symmetric Spaces. , 1973 .

[211]  V. Bangert,et al.  The existence of two closed geodesics on every Finsler 2-sphere , 2007, 0709.1243.

[212]  P. Griffiths,et al.  Characteristics and existence of isometric embeddings , 1983 .

[213]  Thierry Aubin.  The Ricci Curvature , 1998 .

[214]  Michael Gromov,et al.  Curvature, diameter and betti numbers , 1981 .

[215]  G. Huisken,et al.  Convexity estimates for mean curvature flow and singularities of mean convex surfaces , 1999 .

[216]  Yong-Geun Oh,et al.  Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I , 1993 .

[217]  F. Lin,et al.  Geometric measure of singular sets of elliptic equations , 1998 .

[218]  S. Yau,et al.  Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry , 2001, gr-qc/0107094.

[219]  D. Christodoulou.  The instability of naked singularities in the gravitational collapse of a scalar field , 1999, math/9901147.

[220]  Canonical Metrics on the Moduli Space of Riemann Surfaces II , 2004, math/0403068.

[221]  David Mumford,et al.  Geometric invariant theory, Third Edition , 1994, Ergebnisse der Mathematik und ihrer Grenzgebiete.

[222]  Mu-Tao Wang.  A fixed point theorem of discrete group actions on Riemannian manifolds , 1998 .

[223]  Geometry of the Weil-Petersson completion of Teichm\ , 2005, math/0502528.

[224]  B. Chow,et al.  The Ricci flow on surfaces , 2004 .

[225]  John Loftin,et al.  Affine spheres and convex RPn-manifolds , 2001 .

[226]  Kefeng Liu.  HEAT KERNEL AND MODULI SPACE , 2004 .

[227]  Carlos Simpson,et al.  Moduli of representations of the fundamental group of a smooth projective variety I , 1994 .

[228]  An obstruction to the existence of constant scalar curvature K , 2004, math/0412518.

[229]  Symplectic Conifold Transitions , 2002, math/0209319.

[230]  M. Gromov,et al.  The Classification of Simply Connected Manifolds of Positive Scalar Curvature Author ( s ) : , 2010 .

[231]  Lizhen Ji,et al.  Compactifications of Symmetric Spaces , 1998 .

[232]  Jeff Cheeger,et al.  Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds , 1982 .

[233]  Nigel Hitchin,et al.  THE GEOMETRY OF THREE-FORMS IN SIX DIMENSIONS , 2000 .

[234]  Peter B. Gilkey,et al.  Curvature and the eigenvalues of the Laplacian for elliptic complexes , 1973 .

[235]  Hsien-chung Wang.  Complex parallisable manifolds , 1954 .

[236]  P. Kronheimer,et al.  Embedded surfaces and the structure of Donaldson's polynomial invariants , 1995 .

[237]  M. Reid.  The moduli space of 3-folds withK=0 may nevertheless be irreducible , 1987 .

[238]  David L. Webb,et al.  Isospectral plane domains and surfaces via Riemannian orbifolds , 1992 .

[239]  E. Calabi,et al.  The Space of K\"ahler metrics (II) , 2001, math/0108162.

[240]  Richard P. Thomas,et al.  Moment maps, monodromy and mirror manifolds , 2001, math/0104196.

[241]  A. V. Pogorelov.  On the improper convex affine hyperspheres , 1972 .

[242]  H. Verlinde,et al.  Topological strings in d < 1 , 1991 .

[243]  Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial , 2003, hep-th/0306165.

[244]  H. McKean,et al.  Curvature and the Eigenvalues of the Laplacian , 1967 .

[245]  N. Buchdahl.  Hermitian-Einstein connections and stable vector bundles over compact complex surfaces , 1988 .

[246]  Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes , 1993, hep-th/9309140.

[247]  S. Yau,et al.  Differential equations on riemannian manifolds and their geometric applications , 1975 .

[248]  Raoul Bott,et al.  The Yang-Mills equations over Riemann surfaces , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[249]  E. Witten.  On the Structure of the Topological Phase of Two-dimensional Gravity , 1990 .

[250]  S. Donaldson.  Geometry of four-manifolds , 1990 .

[251]  J. King.  The currents defined by analytic varieties , 1971 .

[252]  S. Yau,et al.  The existence of a black hole due to condensation of matter , 1983 .

[253]  M. Gromov.  Metric Structures for Riemannian and Non-Riemannian Spaces , 1999 .

[254]  C. Taubes.  Self-dual Yang-Mills connections on non-self-dual 4-manifolds , 1982 .

[255]  Karsten Grove,et al.  A generalized sphere theorem , 1977 .

[256]  J. Shatah,et al.  Regularity results for nonlinear wave equations , 1993 .

[257]  L. Keen.  COLLARS ON RIEMANN SURFACES , 1974 .

[258]  Karen K. Uhlenbeck.  Removable singularities in Yang-Mills fields , 1979 .

[259]  Gérard Besson,et al.  Entropies et rigidités des espaces localement symétriques de courbure strictement négative , 1995 .

[260]  S. Weinberger.  Aspects of the Novikov conjecture , 1990 .

[261]  J. Nash.  The imbedding problem for Riemannian manifolds , 1956 .

[262]  D. Bao,et al.  An Introduction to Riemann-Finsler Geometry , 2000 .

[263]  L. Saloff-Coste,et al.  A note on Poincaré, Sobolev, and Harnack inequalities , 1992 .

[264]  Shing-Tung Yau,et al.  A lower bound for the heat kernel , 1981 .

[265]  Yoichi Miyaoka,et al.  On the Chern numbers of surfaces of general type , 1977 .

[266]  Y. C. Verdière,et al.  Sur la multiplicité de la première valeur propre non nulle du Laplacien , 1986 .

[267]  J. Cheeger.  A lower bound for the smallest eigenvalue of the Laplacian , 1969 .

[268]  Shing-Tung Yau,et al.  Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds , 1980 .

[269]  M. Atiyah,et al.  Self-duality in four-dimensional Riemannian geometry , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[270]  J. Spruck,et al.  The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian , 1985 .

[271]  S. Yau,et al.  The equivariant Dehn's lemma and loop theorem , 1981 .

[272]  Erwin Lutwak,et al.  L p Affine Isoperimetric Inequalities , 2000 .

[273]  J. Milnor,et al.  EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[274]  M. Murty.  Ramanujan Graphs , 1965 .

[275]  R. Friedman.  Simultaneous resolution of threefold double points , 1986 .

[276]  R. Kobayashi.  Complete Kähler manifolds with zero Ricci curvature and Kobayashi-Ochiai's characterizationof complex projective spaces , 1993 .

[277]  G. Tian,et al.  Stability of complex vector bundles , 1996 .

[278]  Shou-wu Zhang.  Heights and reductions of semi-stable varieties , 1996 .

[279]  J. Demailly.  Regularization of closed positive currents and Intersection Theory , 2007 .

[280]  Peter Li,et al.  On the heat kernel of the Bergmann metric on algebraic varieties , 1995 .

[281]  A generalization of milnor's inequality concerning affine foliations and affine manifolds , 1976 .

[282]  Richard P. Thomas,et al.  Special Lagrangians, stable bundles and mean curvature flow , 2001, math/0104197.

[283]  Mathématiques DE L’I.H.É.S,et al.  Volume and bounded cohomology , 2003 .

[284]  S. Yau,et al.  Harmonic mappings and Kähler manifolds , 1983 .

[285]  S. Bando.  On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature , 1984 .

[286]  Hung-hsi Wu.  The Estimate of the First Eigenvalue of a Compact Riemannian Manifold , 1991 .

[287]  A Degeneration Formula of GW-Invariants , 2001, math/0110113.

[288]  J. Kollár.  Effective base point freeness , 1993 .

[289]  Wolfgang Meyer,et al.  On Complete Open Manifolds of Positive Curvature , 1969 .

[290]  R. Kobayashi,et al.  Ricci-flat Kähler metrics on affine algebraic manifolds , 1990 .

[291]  Thierry Coulhon,et al.  Manifolds and graphs with slow heat kernel decay , 2001 .

[292]  Enumeration of Genus-Two Curves with a Fixed Complex Structure in ℙ 2 and ℙ 3 , 2002, math/0201254.

[293]  J. Sacks,et al.  The Existence of Minimal Immersions of 2-Spheres , 1981 .

[294]  G. Thorbergsson.  Chapter 10 - A Survey on Isoparametric Hypersurfaces and Their Generalizations , 2000 .

[295]  Werner Israel,et al.  Event Horizons in Static Vacuum Space-Times , 1967 .

[296]  Wang Fengyu.  Application of coupling method to the first eigenvalue on manifold , 1995 .

[297]  J. Demailly.  A numerical criterion for very ample line bundles , 1993 .

[298]  C. B. Allendoerfer,et al.  On the cohomology of smooth manifolds , 1958 .

[299]  R. Hamilton,et al.  The formations of singularities in the Ricci Flow , 1993 .

[300]  D. Tataru.  On global existence and scattering for the wave maps equation , 2001 .

[301]  K. Zuo.  Representations of Fundamental Groups of Algebraic Varieties , 2000 .

[302]  Toward a topological characterization of symplectic manifolds , 2002, math/0210103.

[303]  R. Bryant,et al.  On the construction of some complete metrics with exceptional holonomy , 1989 .

[304]  Vacuum configurations for superstrings , 1985 .

[305]  S. Yau,et al.  Calabi's conjecture and some new results in algebraic geometry. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[306]  J. Rosenberg,et al.  C*-algebras, positive scalar curvature, and the Novikov conjecture , 1983 .

[307]  T. Y. Wan.  Constant mean curvature surface, harmonic maps, and universal Teichmüller space , 1992 .

[308]  Y. Ruan.  Topological sigma model and Donaldson-type invariants in Gromov theory , 1996 .

[309]  Jacob Sturm,et al.  The Monge-Ampère operator and geodesics in the space of Kähler potentials , 2005, math/0504157.

[310]  Guoliang Yu.  The Novikov conjecture for groups with finite asymptotic dimension , 1998 .

[311]  John M. Lee,et al.  Einstein metrics with prescribed conformal infinity on the ball , 1991 .

[312]  J. Lohkamp.  Curvature h-principles , 1995 .

[313]  Michael H. Freedman,et al.  The topology of four-dimensional manifolds , 1982 .

[314]  Li Jun.  THE EXISTENCE OF SUPERSYMMETRIC STRING THEORY WITH TORSION , 2004 .

[315]  S. Yau,et al.  From special Lagrangian to Hermitian–Yang–Mills via Fourier–Mukai transform , 2000, math/0005118.

[316]  C. Taubes.  Casson's invariant and gauge theory , 1990 .

[317]  Y. Siu.  Effective very ampleness , 1996 .

[318]  Richard S. Hamilton,et al.  The Ricci flow on surfaces , 1986 .

[319]  B. Shiffman,et al.  A Characterization of Holomorphic Chains , 1974 .

[320]  H. Hofer,et al.  Introduction to Symplectic Field Theory , 2000, math/0010059.

[321]  The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected , 2002, math/0210119.

[322]  L. Simon,et al.  Existence of embedded solutions of Plateau's problem , 1979 .

[323]  Shing-Tung Yau,et al.  Errata to the Paper "Complete Kähler Manifolds with Nonpositive Curvature of Faster than Quadratic Decay" , 1979 .

[324]  C. Taubes.  THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS , 1994 .

[325]  M. Artin.  On Enriques' surfaces , 1960 .

[326]  N. Mok.  An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties , 1984 .

[327]  Robert L. Bryant,et al.  Metrics with exceptional holonomy , 1987 .

[328]  Wilhelm Klingenberg,et al.  Lectures on closed geodesics , 1978 .

[329]  Counting dimensions of L-harmonic functions , 2000, math/0009254.

[330]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[331]  J. Demailly.  Effective bounds for very ample line bundles , 1996 .

[332]  K. Ôno,et al.  ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT , 1999 .

[333]  Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation , 2001, math/0110330.

[334]  Mckenzie Y. Wang,et al.  Existence and non-existence of homogeneous Einstein metrics , 1986 .

[335]  On the complex structure of K\"ahler manifolds with nonnegative curvature , 2005, math/0504422.

[336]  E. Lieb,et al.  On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation , 1976 .

[337]  M. F. Reid.  On boundaries of complex analytic varieties , 1977 .

[338]  G. Huisken.  Flow by mean curvature of convex surfaces into spheres , 1984 .

[339]  Global Existence for the Einstein Vacuum Equations in Wave Coordinates , 2003, math/0312479.

[340]  Shing-Tung Yau,et al.  On univalent harmonic maps between surfaces , 1978 .

[341]  G. Tian,et al.  Floer homology and Arnold conjecture , 1998 .

[342]  S. Klainerman,et al.  CORRIGENDUM: Peeling properties of asymptotically flat solutions to the Einstein vacuum equations , 2004 .

[343]  Mirror Symmetry Without Corrections , 2000, math/0009235.

[344]  Shing-Tung Yau,et al.  On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation , 1980 .

[345]  Brown,et al.  Quasilocal energy and conserved charges derived from the gravitational action. , 1992, Physical review. D, Particles and fields.

[346]  S. Stolz.  Simply connected manifolds of positive scalar curvature , 1990 .

[347]  Einstein type metrics and stability on vector bundles , 1997 .

[348]  Raoul Bott,et al.  On the iteration of closed geodesics and the sturm intersection theory , 1956 .

[349]  Jianguo Cao,et al.  A new 3-dimensional curvature integral formula for PL-manifolds of non-positive curvature , 2003 .

[350]  R. Brooks.  The fundamental group and the spectrum of the laplacian , 1981 .

[351]  ON THE INCOMPLETENESS OF THE WEIL-PETERSSON METRIC ALONG DEGENERATIONS OF CALABI-YAU MANIFOLDS , 1997 .

[352]  Function Theory , 1951, Nature.

[353]  J. Wolf,et al.  Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature , 1971 .

[354]  Chiun-Chuan Chen,et al.  A spherical Harnack inequality for singular solutions of nonlinear elliptic equations , 2001 .

[355]  A. Weinstein.  On the volume of manifolds all of whose geodesics are closed , 1974 .

[356]  Robert L. Bryant,et al.  Conformal and minimal immersions of compact surfaces into the 4-sphere , 1982 .

[357]  I. Singer,et al.  Analytic torsion for complex manifolds , 1973 .

[358]  P. Sarnak.  Spectra of hyperbolic surfaces , 2003 .

[359]  R. Schoen,et al.  Refined asymptotics for constant scalar curvature metrics with isolated singularities , 1998, math/9807038.

[360]  J. Otal.  Thurston's Hyperbolization of Haken Manifolds , 1996 .

[361]  N. Hitchin.  LIE-GROUPS AND TEICHMULLER SPACE , 1992 .

[362]  F. W. Warner,et al.  Existence and Conformal Deformation of Metrics With Prescribed Gaussian and Scalar Curvatures , 1975 .

[363]  Xiaodong Wang,et al.  On the stability of Riemannian manifold with parallel spinors , 2003, math/0311253.

[364]  S. Yau,et al.  Conformally flat manifolds, Kleinian groups and scalar curvature , 1988 .

[365]  Mu-Tao Wang.  Generalized harmonic maps and representations of discrete groups , 2000 .

[366]  Guangyin Wang.  Minimal surfaces in Riemannian manifolds , 1993 .

[367]  G. Tian.  Kähler-Einstein metrics with positive scalar curvature , 1997 .

[368]  M. Boileau,et al.  Uniformization of small 3-orbifolds , 2001 .

[369]  M. Michelsohn.  On the existence of special metrics in complex geometry , 1982 .

[370]  T. Willmore.  EXISTENCE AND REGULARITY OF MINIMAL SURFACES ON RIEMANNIAN MANIFOLDS , 1982 .

[371]  S. Yau.  Splitting theorem and an algebraic geometric characterization of locally Hermitian symmetric spaces , 1993 .

[372]  A. Futaki.  An obstruction to the existence of Einstein Kähler metrics , 1983 .

[373]  R. Melrose.  The inverse spectral problem for planar domains , 1996 .

[374]  J. Marsden,et al.  Reduction of symplectic manifolds with symmetry , 1974 .

[375]  S. Chern,et al.  Characteristic forms and geometric invariants , 1974 .

[376]  W. Goldman,et al.  The classification of real projective structures on compact surfaces , 1997 .

[377]  S. Wolpert.  Disappearance of cusp forms in special families , 1994 .

[378]  R. Bott.  A residue formula for holomorphic vector-fields , 1967 .

[379]  S. Yau,et al.  Three dimensional algebraic manifolds with C1 = 0 and χ = −6 , 1987 .

[380]  Wan-Xiong Shi.  A uniformization theorem for complete Kähler manifolds with positive holomorphic bisectional curvature , 1998 .

[381]  B. Greene,et al.  Mirror manifolds in higher dimension , 1994, hep-th/9402119.

[382]  Rui-Tao Dong.  Nodal sets of eigenfunctions on Riemann surfaces , 1992 .

[383]  F. Lin.  Mapping Problems � Fundamental Groups and Defect Measures , 2003 .

[384]  Y. Tashiro.  Compact four-dimensional Einstein manifolds , 1981 .

[385]  T. Matsusaka.  Polarized Varieties with a Given Hilbert Polynomial , 1972 .

[386]  On the initial-boundary value problem for harmonic maps from the 2-dimensional Minkowksi space , 1980 .

[387]  W. L. Baily,et al.  Compactification of Arithmetic Quotients of Bounded Symmetric Domains , 1966 .

[388]  Toshikazu Sunada,et al.  Riemannian coverings and isospectral manifolds , 1985 .

[389]  C. Fefferman,et al.  The uncertainty principle and sharp gårding inequalities , 1981 .

[390]  D. Phong,et al.  On stability and the convergence of the Kähler-Ricci flow , 2006 .

[391]  Toric Sasaki-Einstein metrics on S2 × S3 , 2005, hep-th/0505027.

[392]  B. Carter.  Global structure of the Kerr family of gravitational fields , 1968 .

[393]  Mu-Tao Wang,et al.  Mathematik in den Naturwissenschaften Leipzig Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials , 2003 .

[394]  André Well.  Sur les théorèmes de de Rham , 1952 .

[395]  S. Yau,et al.  Holomorphic curves in surfaces of general type. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[396]  C. Taubes,et al.  Seiberg-Witten and Gromov invariants for symplectic 4-manifolds , 2005 .

[397]  Karen Uhlenbeck,et al.  Boundary regularity and the Dirichlet problem for harmonic maps , 1983 .

[398]  Wang Changping,et al.  Some examples of complete hyperbolic affine 2-spheres in ℝ3 , 1991 .

[399]  H. Bray.  PROOF OF THE RIEMANNIAN PENROSE INEQUALITY USING THE POSITIVE MASS THEOREM , 2001 .

[400]  S. Donaldson.  Scalar Curvature and Stability of Toric Varieties , 2002 .

[401]  Michael Atiyah,et al.  The moment map and equivariant cohomology , 1984 .

[402]  Jeff Cheeger,et al.  On the structure of spaces with Ricci curvature bounded below. II , 2000 .

[403]  N. Mok,et al.  Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature , 1989 .

[404]  The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains , 2002, math/0210141.

[405]  Y. Siu.  A simple proof of the surjectivity of the period map of K3 surfaces , 1981 .

[406]  R. Schoen,et al.  Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one , 1992 .

[407]  K. Ecker.  Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space , 1997 .

[408]  S. Donaldson.  Symplectic submanifolds and almost-complex geometry , 1996 .

[409]  Gheorghe Lusztig,et al.  Novikov's higher signature and families of elliptic operators , 1972 .

[410]  A. Todorov.  Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces , 1980 .

[411]  H. Choi,et al.  Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space , 1990 .

[412]  R. Schoen.  Conformal deformation of a Riemannian metric to constant scalar curvature , 1984 .

[413]  The symplectic Thom conjecture , 1998, math/9811087.

[414]  S. Yau,et al.  COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME , 1982 .

[415]  The Gauss equations and rigidity of isometric embeddings , 1983 .

[416]  G. Perelman.  Ricci flow with surgery on three-manifolds , 2003, math/0303109.

[417]  V. Guillemin,et al.  The spectrum of positive elliptic operators and periodic bicharacteristics , 1975 .

[418]  R. Wentworth,et al.  Geometric quantization for the moduli space of vector bundles with parabolic structure , 1997 .

[419]  Sheldon Katz,et al.  Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc , 2001 .

[420]  R. Kulkarni.  Conformally flat manifolds. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[421]  Mirror Principle II , 1999, math/9905006.

[422]  Yng-Ing Lee.  Embedded Special Lagrangian Submanifolds in Calabi-Yau Manifolds , 2003 .

[423]  P. Sarnak,et al.  On Selberg's eigenvalue conjecture , 1995 .

[424]  Bartnik,et al.  Particlelike solutions of the Einstein-Yang-Mills equations. , 1988, Physical review letters.

[425]  G. Tian.  Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and Its Peterson-Weil Metric , 1987 .

[426]  K. Smoczyk,et al.  Longtime existence of the Lagrangian mean curvature flow , 2004 .

[427]  S. Yau,et al.  Eigenvalues of elliptic operators and geometric applications , 2004 .

[428]  S. Yau,et al.  Chapter VIII The Equivariant Loop Theorem for Three-Dimensional Manifolds and a Review of the Existence Theorems for Minimal Surfaces , 1984 .

[429]  R. Greene,et al.  Several complex variables and complex geometry , 1991 .

[430]  Howard Garland,et al.  p-Adic Curvature and the Cohomology of Discrete Subgroups of p-Adic Groups , 1973 .

[431]  Jun Li.  Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds , 1996 .

[432]  M. Kuranishi.  Strongly pseudoconvex CR structures over small balls* Part II. A regularity theorem , 1982 .

[433]  K. O’Grady.  The irreducible components of moduli spaces of vector bundles on surfaces , 1993 .

[434]  J. Demailly.  HOLOMORPHIC MORSE INEQUALITIES , 1991 .

[435]  Enrico Bombieri,et al.  Minimal cones and the Bernstein problem , 1969 .

[436]  The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks , 2002, math/0210106.

[437]  Poisson actions and scattering theory for integrable systems , 1997, dg-ga/9707004.

[438]  Y. Matsushima.  On the First Betti Number of Compact Quotient Spaces of Higher-Dimensional Symmetric Spaces , 1962 .

[439]  W. Ballmann,et al.  On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell Complexes , 1997 .

[440]  H. Cao.  On Harnack's inequalities for the Kähler-Ricci flow , 1992 .

[441]  C. Croke,et al.  Some isoperimetric inequalities and eigenvalue estimates , 1980 .

[442]  E. Witten,et al.  Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD , 1994, hep-th/9408099.

[443]  Volume collapsed three-manifolds with a lower curvature bound , 2003, math/0304472.

[444]  C. Fefferman,et al.  On the Bergman kernel and biholomorphic mappings of pseudoconvex domains , 1974 .

[445]  M. Atiyah,et al.  Eta invariants, signature defects of cusps, and values of L-functions , 1983 .

[446]  D. Mumford,et al.  The irreducibility of the space of curves of given genus , 1969 .

[447]  A. Grigor’yan.  THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS , 1992 .

[448]  Robert Connelly.  The rigidity of suspensions , 1978 .

[449]  G. Tian.  On a set of polarized Kähler metrics on algebraic manifolds , 1990 .

[450]  C. Simpson.  Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization , 1988 .

[451]  Tian-Jun Li.  SYMPLECTIC 4-MANIFOLDS WITH KODAIRA DIMENSION ZERO , 2006 .

[452]  H. Lawson.  Local Rigidity Theorems for Minimal Hypersurfaces , 1969 .

[453]  Y. Siu,et al.  Geometric superrigidity , 1993 .

[454]  Changshou Lin.  The local isometric embedding in R3 of two‐dimensional riemannian manifolds with gaussian curvature changing sign cleanly , 1986 .

[455]  N. Nadirashvili,et al.  How large can the first eigenvalue be on a surface of genus two , 2005, math/0509398.

[456]  Jun Li,et al.  Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties , 1996 .

[457]  B. M. Fulk.  MATH , 1992 .

[458]  Singularities of special Lagrangian fibrations and the SYZ Conjecture , 2000, math/0011179.

[459]  Enumeration of Rational Curves Via Torus Actions , 1994, hep-th/9405035.

[460]  Shing-Tung Yau,et al.  On the regularity of the monge‐ampère equation det (∂2 u/∂xi ∂xj) = f(x, u) , 1977 .

[461]  S. Donaldson.  REMARKS ON GAUGE THEORY, COMPLEX GEOMETRY AND 4-MANIFOLD TOPOLOGY , 1997 .

[462]  C. Taubes.  The existence of anti-self-dual conformal structures , 1992 .

[463]  S. Yau,et al.  Positivity of the Total Mass of a General Space-Time , 1979 .

[464]  Mean Curvature Flow of Surfaces in Einstein Four-Manifolds , 2001, math/0110019.

[465]  G. Szegő,et al.  Inequalities for Certain Eigenvalues of a Membrane of Given Area , 1954 .

[466]  Y. Egorov,et al.  Fourier Integral Operators , 1994 .

[467]  J. Morgan,et al.  On Thurston''s uniformization theorem for three-dimensional manifolds , 1984 .

[468]  R. Hamilton.  Non-singular solutions of the Ricci flow on three-manifolds , 1999 .

[469]  Shôshichi Kobayashi,et al.  Meromorphic mappings onto compact complex spaces of general type , 1975 .

[470]  K. Jörgens.  Über die Lösungen der Differentialgleichungrt−s2=1 , 1954 .

[471]  C. T. Yang.  Smooth great circle fibrations and an application to the topological Blaschke conjecture , 1990 .

[472]  C. Taubes.  SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves , 1996 .

[473]  Robert Osserman,et al.  A Proof of the Regularity Everywhere of the Classical Solution to Plateau's Problem , 1970 .

[474]  Dusa McDuff,et al.  The geometry of symplectic energy , 1993 .

[475]  R. Hardt,et al.  Minimal surfaces with isolated singularities , 1984 .

[476]  Szego kernels and a theorem of Tian , 2000, math-ph/0002009.

[477]  M. Atiyah,et al.  Construction of Instantons , 1978 .

[478]  M. Goresky,et al.  Weighted cohomology , 1994 .

[479]  S. Yau,et al.  Estimates of eigenvalues of a compact Riemannian manifold , 1980 .

[480]  Iteration on Teichmüller space , 1990 .

[481]  Hyeong In Choi,et al.  The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature , 1985 .

[482]  Xiuxiong Chen.  The Space of Kähler Metrics , 2000 .

[483]  Spectral asymmetry and Riemannian geometry I , 1975 .

[484]  S. Yau,et al.  Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres , 1974 .

[485]  M. Kuranishi.  Strongly Pseudoconvex CR Structures over Small Balls Part III. An Embedding Theorem , 1982 .

[486]  A. Beauville,et al.  Variétés Kähleriennes dont la première classe de Chern est nulle , 1983 .

[487]  Hung-hsi Wu.  Curvature Characterization of Compact Hermitian Symmetric Spaces , 1991 .

[488]  V. Guillemin.  Wave-trace invariants , 1996 .

[489]  S. Bando,et al.  Uniqueness of Einstein Kähler Metrics Modulo Connected Group Actions , 1987 .

[490]  Peter Li,et al.  Complete manifolds with positive spectrum, II , 2001 .

[491]  L. Evans,et al.  Motion of level sets by mean curvature. II , 1992 .

[492]  L. B. Monvel,et al.  Sur la singularité des noyaux de Bergman et de Szegö , 1975 .

[493]  R. Bartnik.  Quasi-spherical metrics and prescribed scalar curvature , 1993 .

[494]  E. Cartan.  Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques , 1939 .

[495]  N. Trudinger,et al.  The Bernstein problem for affine maximal hypersurfaces , 2000 .

[496]  Hong-Jong Kim.  Proceedings of GARC Workshop on geometry and topology '93 , 1993 .

[497]  C. Voisin.  On the homotopy types of compact Kähler and complex projective manifolds , 2003, math/0312032.

[498]  H. Weyl.  Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung) , 1912 .

[499]  Shôshichi Kobayashi.  Intrinsic metrics on complex manifolds , 1967 .

[500]  Michael Wolf.  The Teichmüller theory of harmonic maps , 1989 .

[501]  A. Nadel.  Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature , 1990 .

[502]  S. Yau.  On the Fundamental Group of Compact Manifolds of Non-Positive Curvature , 1971 .

[503]  A new construction of compact 8-manifolds with holonomy ${\rm Spin}(7)$ , 1999, math/9910002.

[504]  M. Micallef,et al.  Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes , 1988 .

[505]  A Uniformization Theorem For Complete Non-compact Kähler Surfaces With Positive Bisectional Curvature , 2002, math/0211372.

[506]  S. Yau,et al.  Compact kähler manifolds of positive bisectional curvature , 1980 .

[507]  S. Donaldson,et al.  Floer’s work on instanton homology, knots and surgery , 1995 .

[508]  James Simons,et al.  Differential characters and geometric invariants , 1985 .

[509]  A. Todorov.  The Weil-Petersson geometry of the moduli space ofSU(n≧3) (Calabi-Yau) manifolds I , 1989 .

[510]  Shiing-Shen Chern,et al.  Characteristic Classes of Hermitian Manifolds , 1946 .

[511]  F. Kirwan,et al.  Localization and the quantization conjecture , 1997 .

[512]  Karen Uhlenbeck,et al.  Bäcklund transformations and loop group actions , 1998, math/9805074.

[513]  S. Yau,et al.  On the isoperimetric inequality for minimal surfaces , 1984 .

[514]  S. Yau,et al.  Some Remarks on the Quasi - local Mass , 1988 .

[515]  S. Yau,et al.  Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature , 1996 .

[516]  Shing-Tung Yau,et al.  HEAT-EQUATIONS ON MINIMAL SUBMANIFOLDS AND THEIR APPLICATIONS , 1984 .

[517]  T. Fujita.  On Polarized Manifolds Whose Adjoint Bundles Are Not Semipositive , 1987 .

[518]  M. Mulase.  KP Equations, Strings, and the Schottky Problem , 1988 .

[519]  Karen K. Uhlenbeck,et al.  On the existence of hermitian‐yang‐mills connections in stable vector bundles , 1986 .

[520]  R. Macpherson,et al.  Geometry of compactifications of locally symmetric spaces , 2002 .

[521]  J. Eells,et al.  Harmonic Mappings of Riemannian Manifolds , 1964 .

[522]  D. Sullivan,et al.  The homology theory of the closed geodesic problem , 1976 .

[523]  D. joyce.  COMPACT RIEMANNIAN 7-MANIFOLDS WITH HOLONOMY G2. I , 2004 .

[524]  W. Ballmann.  On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature , 1989 .

[525]  Y. Oh,et al.  Zero-loop open strings in the cotangent bundle and Morse homotopy , 1997 .

[526]  The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature , 1988 .

[527]  Intersection theory of coassociative submanifolds in G_(2)-manifolds and Seiberg-Witten invariants , 2004, math/0401419.

[528]  Connectedness of the boundary in the AdS / CFT correspondence , 1999, hep-th/9910245.

[529]  S. Donaldson.  An application of gauge theory to four-dimensional topology , 1983 .

[530]  A. Floer,et al.  Morse theory for Lagrangian intersections , 1988 .

[531]  Shing-Tung Yau,et al.  ON THE UPPER ESTIMATE OF THE HEAT KERNEL OF A COMPLETE RIEMANNIAN MANIFOLD , 1981 .

[532]  Eckart Viehweg,et al.  Quasi-projective moduli for polarized manifolds , 1995, Ergebnisse der Mathematik und ihrer Grenzgebiete.

[533]  S. Yau,et al.  THE CLASSICAL PLATEAU PROBLEM AND THE TOPOLOGY OF THREE-DIMENSIONAL MANIFOLDS , 1982 .

[534]  E. Looijenga.  L2-cohomology of locally symmetric varieties , 1988 .

[535]  B. Greene,et al.  Duality in {Calabi-Yau} Moduli Space , 1990 .

[536]  D. Gieseker.  Global moduli for surfaces of general type , 1977 .

[537]  Chuan-Gan Hu,et al.  Normal families of holomorphic mappings , 1992 .

[538]  Tian-Jun Li,et al.  Symplectic structure on ruled surfaces and a generalized adjunction formula , 1995 .

[539]  W. Thurston,et al.  Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.

[540]  S. Yau,et al.  Curvature estimates for minimal hypersurfaces , 1975 .

[541]  Yun-Gang Chen,et al.  Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations , 1989 .

[542]  Luis A. Caffarelli,et al.  The Dirichlet problem for nonlinear second-order elliptic equations I , 1984 .

[543]  P. Chruściel.  Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation , 1991 .

[544]  T. Aubin.  Equations differentielles non lineaires et probleme de Yamabe concernant la courbure scalaire , 1976 .

[545]  W. Ballmann,et al.  Closed geodesics on positively curved manifolds , 1982 .

[546]  A. Liu.  Some New applications of General Wall Crossing Formula, Gompf’s Conjecture and its Applications , 1996 .

[547]  Xiping Zhu,et al.  Complete Riemannian manifolds with pointwise pinched curvature , 2000 .

[548]  Deforming Area Preserving Diffeomorphism of Surfaces by Mean Curvature Flow , 2001, math/0110020.

[549]  Shing-Tung Yau,et al.  An Estimate of the Gap of the First Two Eigenvalues in the Schr , 2009, 0902.2250.

[550]  D. Sullivan,et al.  Function theory, random paths and covering spaces , 1984 .

[551]  R. Schoen,et al.  Positive harmonic functions on complete manifolds of negative curvature , 1985 .

[552]  C. Taubes.  S1 actions and elliptic genera , 1989 .

[553]  Wan-Xiong Shi.  Complete noncompact Kähler manifolds with positive holomorphic bisectional curvature , 1990 .

[554]  M. Hopkins.  Topological Modular Forms, the Witten Genus, and the Theorem of the Cube , 1995 .

[555]  D. Sullivan.  Cycles for the dynamical study of foliated manifolds and complex manifolds , 1976 .

[556]  W. Meeks,et al.  The uniqueness of the helicoid , 2005 .

[557]  Leon Simon,et al.  Theorems on Regularity and Singularity of Energy Minimizing Maps , 1996 .

[558]  V. K. Patodi,et al.  On the heat equation and the index theorem , 1973 .

[559]  M. Berger.  Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes , 1955 .

[560]  S. Yau.  On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I* , 1978 .

[561]  Negatively curved manifolds with exotic smooth structures , 1989 .

[562]  A. Floer.  WITTEN'S COMPLEX AND INFINITE DIMENSIONAL MORSE THEORY , 1989 .

[563]  Eugenio Calabi,et al.  Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens. , 1958 .

[564]  Shing-Tung Yau,et al.  Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces , 1976 .

[565]  C. Lebrun,et al.  Explicit Self-dual Metrics on Cp 2 # #cp 2 , 1991 .

[566]  On the polynomial cohomology of affine manifolds , 1982 .

[567]  R. Schoen,et al.  Minimizing area among Lagrangian surfaces: The mapping problem , 2000, math/0008244.

[568]  H. Hofer.  On the topological properties of symplectic maps , 1990, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[569]  A. Freire.  On the Martin boundary of Riemannian products , 1991 .

[570]  Gradient estimates and blow-up analysis for stationary harmonic maps , 1999, math/9905214.

[571]  R. Greene,et al.  Differential Geometry: Partial Differential Equations on Manifolds , 1993 .

[572]  C. McMullen.  The moduli space of Riemann surfaces is Kähler hyperbolic , 2000, math/0010022.

[573]  Jun Li,et al.  Irreducibility of moduli of rank-2 vector bundles on algebraic surfaces , 1994 .

[574]  M. C. Dafermos.  Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations , 2001 .

[575]  Shigefumi Mori,et al.  Proj ective manifolds with ample tangent bundles , 1979 .

[576]  M. Lübke.  Stability of Einstein-Hermitian vector bundles , 1983 .

[577]  Kefeng Liu.  On modular invariance and rigidity theorems , 1995 .

[578]  J. Bismut,et al.  Symplectic geometry and the Verlinde Formulas , 1999 .

[579]  R. Bartnik.  Existence of maximal surfaces in asymptotically flat spacetimes , 1984 .

[580]  Hua Luo.  Geometric criterion for Gieseker-Mumford stability of polarized manifolds , 1998 .

[581]  J. Cheeger,et al.  Collapsing riemannian manifolds while keeping their curvature bounded. I. , 1986 .

[582]  Kenneth A. Brakke,et al.  The motion of a surface by its mean curvature , 2015 .

[583]  J. Cheeger,et al.  The splitting theorem for manifolds of nonnegative Ricci curvature , 1971 .

[584]  S. Donaldson,et al.  Connected sums of self-dual manifolds and deformations of singular spaces , 1989 .

[585]  Shiu-yuen Cheng,et al.  Eigenvalue comparison theorems and its geometric applications , 1975 .

[586]  N. Wallach,et al.  Minimal immersions of spheres into spheres. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[587]  H. Choi,et al.  A first eigenvalue estimate for minimal hypersurfaces , 1983 .

[588]  J. Bismut.  The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs , 1986 .

[589]  S. Donaldson.  Scalar Curvature and Projective Embeddings, I , 2001 .

[590]  L. Simon.  Regularity Theory for Harmonic Maps , 1996 .

[591]  The Fukaya category of symplectic neighborhood of a non-Hausdorff manifold , 2006, math/0602119.

[592]  V. Bangert,et al.  ON THE EXISTENCE OF CLOSED GEODESICS ON TWO-SPHERES , 1993 .

[593]  Existence of Supersymmetric Hermitian Metrics with Torsion on Non-Kaehler Manifolds , 2005, hep-th/0509028.

[594]  W. Schmid.  Variation of hodge structure: The singularities of the period mapping , 1973 .

[595]  M. Micallef.  Stable minimal surfaces in Euclidean space , 1984 .

[596]  G. Pólya,et al.  Isoperimetric inequalities in mathematical physics , 1951 .

[597]  An application of eigenvalue estimate to algebraic curves defined by congruence subgroups , 1996 .

[598]  S. Yau,et al.  Hermitian-Yang-Mills Connection on Non-Kähler Manifolds , 1987 .

[599]  S. Yau.  Nonlinear Analysis In Geometry , 1986 .

[600]  Christopher B. Croke.  A sharp four dimensional isoperimetric inequality , 1984 .

[601]  S. Donaldson.  Infinite determinants, stable bundles and curvature , 1987 .

[602]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[603]  N. Kuiper,et al.  On C1-isometric imbeddings. II , 1955 .

[604]  F. Lin.  Asymptotic behavior of area-minimizing currents in hyperbolic space , 1989 .

[605]  Chung-Tao Yang.  Any Blaschke manifold of the homotopy type of ${\bf C}{\rm P}^n$ has the right volume. , 1991 .

[606]  Jürgen Jost,et al.  Convex functionals and generalized harmonic maps into spaces of non positive curvature , 1995 .

[607]  Shing-Tung Yau,et al.  On the proof of the positive mass conjecture in general relativity , 1979 .

[608]  J. Taylor,et al.  Almgren's big regularity paper : Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2 , 2000 .

[609]  L(2)-cohomology of arithmetic varieties. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[610]  D. Sullivan,et al.  Real homotopy theory of Kähler manifolds , 1975 .

[611]  S. Yau,et al.  COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE , 1982 .

[612]  Shiing-Shen Chern,et al.  Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length , 1970 .

[613]  J. Jost.  Embedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball or sphere , 1989 .

[614]  D. Sullivan.  The Dirichlet problem at infinity for a negatively curved manifold , 1983 .

[615]  G. Tian.  Gauge theory and calibrated geometry, I , 2000, math/0010015.

[616]  J. Mawhin,et al.  Nondegenerate Critical Manifolds , 1989 .

[617]  The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks , 2002, math/0210086.

[618]  C. Lütken,et al.  Complete intersection Calabi-Yau manifolds , 1988 .

[619]  Nigel Hitchin.  Stable forms and special metrics , 2001 .

[620]  Pengfei Guan,et al.  The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equation , 2003 .

[621]  S. Yau,et al.  Lectures on Differential Geometry , 1994 .

[622]  Neil S. Trudinger,et al.  Remarks concerning the conformal deformation of riemannian structures on compact manifolds , 1968 .

[623]  E. Lutwak.  Selected Affine Isoperimetric Inequalities , 1993 .

[624]  D. Epstein,et al.  Three-dimensional manifolds , 1960 .

[625]  Y. Siu,et al.  Very ampleness part of Fujita’s conjecture and multiplier ideal sheaves of Kohn and Nadel , 2001 .

[626]  Spectral and scattering theory for symbolic potentials of order zero , 2001, math/0112163.

[627]  M. Gromov,et al.  Partial Differential Relations , 1986 .

[628]  R. Lazarsfeld,et al.  Global generation of pluricanonical and adjoint linear series on smooth projective threefolds , 1993 .

[629]  Christian Bär.  ON HARMONIC SPINORS , 1998 .

[630]  Jun Li.  Algebraic geometric interpretation of Donaldson's polynomial invariants , 1993 .

[631]  Embedded minimal surfaces , 2006, math/0601176.

[632]  P. Lu,et al.  The complex structure on a connected sum ofS3×S3 with trivial canonical bundle , 1994 .

[633]  P. Deligne.  Theorie de Hodge I , 1970 .

[634]  Equivariant Gromov - Witten Invariants , 1996, alg-geom/9603021.

[635]  Mckenzie Y. Wang,et al.  Metrics with nonnegative isotropic curvature , 1993 .

[636]  R. Hardt,et al.  Critical sets of solutions to elliptic equations , 1999 .

[637]  D. C. Robinson.  Uniqueness of the Kerr black hole , 1975 .

[638]  J. Rubinstein,et al.  Equivariant minimax and minimal surfaces in geometric three-manifolds , 1988 .

[639]  Shôshichi Kobayashi.  On Compact Kahler Manifolds with Positive Definite Ricci Tensor , 1961 .

[640]  A. Givental.  A mirror theorem for toric complete intersections , 1997, alg-geom/9701016.

[641]  S. Yau,et al.  Special Lagrangian fibrations II: Geometry. A survey of techniques in the study of special Lagrangian fibrations , 2001 .

[642]  V. K. Patodi,et al.  Spectral asymmetry and Riemannian Geometry. I , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[643]  Xenia de la Ossa,et al.  A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory , 1991 .

[644]  An eigenvalue bound for compact manifolds with varying curvature , 1989 .

[645]  Maxim Kontsevich,et al.  Homological Algebra of Mirror Symmetry , 1994, alg-geom/9411018.

[646]  S. Donaldson.  The Seiberg-Witten equations and 4-manifold topology , 1996 .

[647]  Chiu-Chu Melissa Liu.  Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair , 2002, math/0210257.

[648]  S. Yau,et al.  On the parabolic kernel of the Schrödinger operator , 1986 .

[649]  D. Lüst,et al.  Heterotic string theory on non‐Kähler manifolds with H‐flux and Gaugino condensate , 2003, hep-th/0310021.

[650]  C. Taubes.  Self-dual connections on 4-manifolds with indefinite intersection matrix , 1984 .

[651]  Vaughan F. R. Jones,et al.  Hecke algebra representations of braid groups and link polynomials , 1987 .

[652]  S. Donaldson.  Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles , 1985 .

[653]  F. Chung.  Discrete isoperimetric inequalities , 1996 .

[654]  C. S. Gardner,et al.  Korteweg-devries equation and generalizations. VI. methods for exact solution , 1974 .

[655]  L. Nirenberg.  The Weyl and Minkowski problems in differential geometry in the large , 1953 .

[656]  N. Leung,et al.  Geometric structures on G2 and Spin (7)-manifolds , 2002, math/0202045.

[657]  J. Duistermaat,et al.  On the variation in the cohomology of the symplectic form of the reduced phase space , 1982 .

[658]  Kuo-Tsai Chen.  Differential forms and homotopy groups , 1971 .

[659]  Kefeng Liu.  On elliptic genera and theta-functions , 1996 .

[660]  Robert E. Gompf.  A new construction of symplectic manifolds , 1995 .

[661]  A mathematical theory of the topological vertex , 2004, math/0408426.

[662]  E. Davies,et al.  Gaussian upper bounds for the heat kernels of some second-order operators on Riemannian manifolds , 1988 .

[663]  J. Jorgenson,et al.  Enriques Surfaces, Analytic Discriminants, and Borcherds's Φ Function , 1998 .

[664]  C. Fefferman,et al.  Nodal sets of eigenfunctions on Reimannian manifolds , 1988 .

[665]  E. Zehnder,et al.  The dynamics on three-dimensional strictly convex energy surfaces , 1998 .

[666]  GENERALIZED SPECIAL LAGRANGIAN TORUS FIBRATION FOR CALABI-YAU HYPERSURFACES IN TORIC VARIETIES I , 2003, math/0303114.