Harmonic maps: Dedicated to the memory of James Eells

[1]  Robert Gulliver,et al.  A Theory of Branched Immersions of Surfaces , 1973 .

[2]  Rui Pacheco,et al.  Twistor fibrations giving primitive harmonic maps of finite type , 2005, Int. J. Math. Math. Sci..

[3]  Brian White,et al.  Homotopy classes in Sobolev spaces and the existence of energy minimizing maps , 1988 .

[4]  Ulrich Pinkall,et al.  On the classification of constant mean curvature tori , 1989 .

[5]  Harmonic two-spheres in compact symmetric spaces, revisited , 1996, dg-ga/9606002.

[6]  Lawrence C. Evans,et al.  Partial regularity for stationary harmonic maps into spheres , 1991 .

[7]  L. Simon.  Rectifiability of the singular set of energy minimizing maps , 1995 .

[8]  A. Soyeur,et al.  The Dirichlet problem for harmonic maps from the disc into the 2-sphere , 1989, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[9]  Jean-Michel Coron,et al.  Harmonic maps with defects , 1986 .

[10]  Edmund Taylor Whittaker,et al.  On the General Solution of Laplace's Equation and the Equation of Wave Motions, and on an undulatory explanation of Gravity , 1902 .

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

[12]  R. T. Smith.  Harmonic Mappings of Spheres , 1975 .

[13]  Chang Kungching,et al.  Heat flow and boundary value problem for harmonic maps , 1989 .

[14]  Richard S. Hamilton,et al.  Harmonic Maps of Manifolds with Boundary , 1975 .

[15]  Luc Lemaire,et al.  Applications harmoniques de surfaces riemanniennes , 1978 .

[16]  Petru Mironescu,et al.  Lifting in Sobolev spaces , 2000 .

[17]  J. Dorfmeister,et al.  Weierstrass type representation of harmonic maps into symmetric spaces , 1998 .

[18]  Michael Wiegner.  Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme , 1976 .

[19]  Francis E. Burstall.  Harmonic Maps of Finite Energy From Non-Compact Manifolds , 1984 .

[20]  James Eells,et al.  Harmonic Maps and Minimal Immersions with Symmetries , 1993 .

[21]  J. Eells,et al.  A Report on Harmonic Maps , 1978 .

[22]  Karen Uhlenbeck,et al.  Regularity of minimizing harmonic maps into the sphere , 1984 .

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

[24]  Jean-Michel Coron,et al.  A Cohomological Criterion for Density of Smooth Maps in Sobolev Spaces Between Two Manifolds , 1991 .

[25]  James Eells,et al.  Restrictions on harmonic maps of surfaces , 1976 .

[26]  F. Lin,et al.  A remark on the map x/[x] , 1987 .

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

[28]  Martin Fuchs,et al.  p-Harmonic obstacle problems , 1990 .

[29]  CONSTRUCTION OF HARMONIC MAPS BETWEEN SPHERES BY JOINING THREE EIGENMAPS , 1998 .

[30]  Enrico Giusti,et al.  On the regularity of the minima of variational integrals , 1982 .

[31]  Jean-Michel Coron,et al.  Multiple solutions of H‐systems and Rellich's conjecture , 1984 .

[32]  C. Taubes.  The existence of a non-minimal solution to the SU (2) Yang-Mills-Higgs equations on ℝ3. Part I , 1982 .

[33]  F. Lin,et al.  Energy quantization for harmonic maps , 2002 .

[34]  F. Béthuel,et al.  Density of Smooth Functions between Two Manifolds in Sobolev Spaces , 1988 .

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

[36]  Hermann Karcher,et al.  Non-existence results and growth properties for harmonic maps and forms. , 1984 .

[37]  Yunmei Chen,et al.  The weak solutions to the evolution problems of harmonic maps , 1989 .

[38]  Lihe Wang,et al.  Regularity of harmonic maps , 1999 .

[39]  Jie Qing,et al.  On singularities of the heat flow for harmonic maps from surfaces into spheres , 1995 .

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

[41]  Robert Gulliver,et al.  Minimizing p-harmonic maps into spheres. , 1989 .

[42]  Haim Brezis,et al.  Regularity of minimizers of relaxed problems for harmonic maps , 1991 .

[43]  Nonunique tangent maps at isolated singularities of harmonic maps , 1992, math/9201270.

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

[45]  James Eells,et al.  Harmonic maps from surfaces to complex projective spaces , 1983 .

[46]  Jiří Souček,et al.  The dirichlet energy of mappings with values into the sphere , 1989 .

[47]  Convergence of minimizers for thep-Dirichlet integral , 1993 .

[48]  H. Brezis,et al.  Topology and Sobolev Spaces , 2000 .

[49]  Michael Struwe,et al.  On the evolution of harmonic maps in higher dimensions , 1988 .

[50]  E. Stein,et al.  Hp spaces of several variables , 1972 .

[51]  J. Eells,et al.  Another Report on Harmonic Maps , 1988 .

[52]  B. Fuglede.  Harmonic morphisms between riemannian manifolds , 1978 .

[53]  Alexander I. Bobenko,et al.  All constant mean curvature tori inR3,S3,H3 in terms of theta-functions , 1991 .

[54]  E. Lieb,et al.  Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds , 1988 .

[55]  L. Lemaire,et al.  On the space of harmonic 2-spheres in CP2 , 1996 .

[56]  Connected sums of constant mean curvature surfaces in Euclidean 3 space , 1999, math/9905077.

[57]  Andrea Ratto,et al.  HARMONIC MAPS OF SPHERES AND THE HOPF CONSTRUCTION , 1989 .

[58]  Simon Salamon,et al.  Twistorial construction of harmonic maps of surfaces into four-manifolds , 1985 .

[59]  J. Qing.  Remark on the Dirichlet problem for harmonic maps from the disc into the 2-sphere , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[60]  Jürgen Jost,et al.  Existence proofs for harmonic mappings with the help of a maximum principle , 1983 .

[61]  Karen Uhlenbeck,et al.  Connections withLP bounds on curvature , 1982 .

[62]  J. Rawnsley,et al.  Twistor Theory for Riemannian Symmetric Spaces , 1990 .

[63]  David Kinderlehrer,et al.  Existence and partial regularity of static liquid crystal configurations , 1986 .

[64]  J. Dorfmeister,et al.  Pluriharmonic Maps, Loop Groups and Twistor Theory , 2003 .

[65]  J. Rubinstein,et al.  Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents , 1996 .

[66]  Jean-Michel Coron,et al.  Large solutions for harmonic maps in two dimensions , 1983 .

[67]  Elias M. Stein,et al.  On the theory of harmonic functions of several variables , 1960 .

[68]  Michael Struwe,et al.  Partial regularity for harmonic maps and related problems , 2006, math/0604635.

[69]  Stefan Hildebrandt,et al.  An existence theorem for harmonic mappings of Riemannian manifolds , 1977 .

[70]  Eugenio Calabi,et al.  Minimal immersions of surfaces in Euclidean spheres , 1967 .

[71]  Y. Meyer,et al.  Compensated compactness and Hardy spaces , 1993 .

[72]  F. John,et al.  On functions of bounded mean oscillation , 1961 .

[73]  J. Eells,et al.  Selected topics on harmonic maps , 1983 .

[74]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[75]  Henri Poincaré,et al.  Sur les Equations aux Derivees Partielles de la Physique Mathematique , 1890 .

[76]  H. Fédérer,et al.  The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension , 1970 .

[77]  Michael Struwe.  Uniqueness of harmonic maps with small energy , 1998 .

[78]  Stefan Hildebrandt,et al.  On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order , 1977 .

[79]  Harmonic morphisms with fibers of dimension one , 1997, dg-ga/9701002.

[80]  Toru Ishihara,et al.  A mapping of Riemannian manifolds which preserves harmonic functions , 1979 .

[81]  Robert Hardt,et al.  Singularities of harmonic maps , 1997 .

[82]  Michael Struwe,et al.  On the evolution of harmonic mappings of Riemannian surfaces , 1985 .

[83]  Stephan Luckhaus,et al.  Partial hölder continuity for minima of certain energies among maps into a Riemannian manifold , 1988 .

[84]  Mariano Giaquinta,et al.  A priori estimates for harmonic mappings. , 1982 .

[85]  Elliott H. Lieb,et al.  Co-Area, Liquid Crystals, and Minimal Surfaces , 1988 .

[86]  Jie Qing,et al.  Bubbling of the heat flows for harmonic maps from surfaces , 1997 .

[87]  F. Lin,et al.  A remark on H1 mappings , 1986 .

[88]  Philip Hartman,et al.  On Homotopic Harmonic Maps , 1967, Canadian Journal of Mathematics.

[89]  François Murat.  Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant , 1981 .

[90]  Frédéric Hélein,et al.  Harmonic Maps, Conservation Laws, And Moving Frames , 2002 .

[91]  Fanghua Lin,et al.  Remarks on approximate harmonic maps , 1995 .

[92]  Fengbo Hang.  Density problems for W1,1 (M, N) , 2002 .

[93]  Jalal Shatah,et al.  Weak solutions and development of singularities of the SU(2) σ‐model , 1988 .

[94]  J. Qing.  Multiple solutions of the Dirichlet problem for harmonic maps from discs into 2-spheres , 1992 .

[95]  F. Lin,et al.  Axially symmetric harmonic maps minimizing a relaxed energy , 1992 .

[96]  Brian White,et al.  Infima of energy functionals in homotopy classes of mappings , 1986 .

[97]  Thomas H. Parker.  Bubble tree convergence for harmonic maps , 1996 .

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

[99]  Libin Mou,et al.  Regularity forn-harmonic maps , 1996 .

[100]  Frédéric Hélein,et al.  Regularity of weakly harmonic maps from a surface into a manifold with symmetries , 1991 .

[101]  P-harmonic obstacle problems , 1989 .

[102]  K. Pohlmeyer,et al.  Integrable Hamiltonian systems and interactions through quadratic constraints , 1976 .

[103]  George D. Birkhoff,et al.  Dynamical systems with two degrees of freedom , 1917 .

[104]  E. Kuwert.  Minimizing the energy of maps from a surface into a 2-sphere with prescribed degree and boundary values , 1994 .

[105]  Shiing-Shen Chern,et al.  Minimal Surfaces in an Euclidean Space of N Dimensions , 1965 .

[106]  Jürgen Jost,et al.  The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values , 1984 .

[107]  A. Freire.  Uniqueness for the harmonic map flow from surfaces to general targets , 1995 .

[108]  J. Sacks,et al.  The existence of minimal immersions of two-spheres , 1977 .

[109]  Willi Jäger,et al.  Uniqueness and stability of harmonic maps and their Jacobi fields , 1979 .

[110]  Stefan Hildebrandt,et al.  Harmonic mappings into Riemannian manifolds with non-positive sectional curvature. , 1975 .

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

[112]  R. Hardt,et al.  Connecting topological Hopf singularities , 2003 .

[113]  Nicolaos Kapouleas.  Complete constant mean curvature surfaces in euclidean three-space , 1990 .

[114]  Willi Jäger,et al.  Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems. , 1983 .

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

[116]  J. Rawnsley,et al.  F-structures, F-twistor spaces and harmonic maps , 1985 .

[117]  Roger Penrose,et al.  Solutions of the Zero-Rest-Mass Equations , 1969 .

[118]  Andrea Ratto,et al.  Existence and non-existence results for harmonic maps between spheres , 1990 .

[119]  Jean-Michel Coron,et al.  Nonuniqueness for the heat flow of harmonic maps , 1990 .

[120]  Michael Grüter,et al.  Regularity of weak H-surfaces. , 1981 .

[121]  E. Ruh,et al.  The tension field of the Gauss map , 1970 .

[122]  Jürgen Jost,et al.  Morse-Conley theory for minimal surfaces of varying topological type , 1990 .

[123]  F. Béthuel.  On the singular set of stationary harmonic maps , 1993 .

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

[125]  Regularity theory for minimizing equivariant ( $p$–)harmonic mappings , 1998 .

[126]  T. Rivière.  Conservation laws for conformally invariant variational problems , 2006, math/0603380.

[127]  T. Rivière.  Dense Subsets of H1/2(S2, S1) , 2000 .

[128]  M. Giaquinta.  Cartesian currents in the calculus of variations , 1983 .

[129]  M. Guest.  Harmonic Maps, Loop Groups, and Integrable Systems: Acknowledgements , 1997 .

[130]  Robert Hardt,et al.  The singular set of an energy minimizing map fromB4 toS2 , 1990 .

[131]  Sagun Chanillo,et al.  Sobolev inequalities involving divergence free maps , 1991 .

[132]  Pierre-Louis Lions,et al.  The concentration-compactness principle in the Calculus of Variations , 1985 .

[133]  Peter M. Topping,et al.  Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow , 2004 .

[134]  A. Sergeev,et al.  Twistor spaces and harmonic maps , 1993 .

[135]  J. Eschenburg,et al.  Associated families of pluriharmonic maps¶and isotropy , 1998 .

[136]  Richard S. Palais,et al.  The principle of symmetric criticality , 1979 .

[137]  Henry C. Wente.  Counterexample to a conjecture of H. Hopf , 1986 .

[138]  Henry C. Wente.  An existence theorem for surfaces of constant mean curvature , 1969 .

[139]  Luc Tartar,et al.  The Compensated Compactness Method Applied to Systems of Conservation Laws , 1983 .

[140]  H. Brezis,et al.  Degree and Sobolev spaces , 1999 .

[141]  M. Gromov,et al.  Embeddings and immersions in Riemannian geometry , 1970 .

[142]  Karen Uhlenbeck,et al.  Harmonic maps; a direct method in the calculus of variations , 1970 .

[143]  L. Simon.  Asymptotics for a class of non-linear evolution equations, with applications to geometric problems , 1983 .

[144]  M. R. Pakzad,et al.  Weak density of smooth maps for the Dirichlet energy between manifolds , 2003 .

[145]  Paul Baird,et al.  A conservation law for harmonic maps , 1981 .

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

[147]  C. Constantinescu,et al.  Potential theory on harmonic spaces , 1972 .

[148]  Haim Brezis,et al.  The interplay between analysis and topology in some nonlinear PDE problems , 2003 .

[149]  C. Jacobi.  Über eine particuläre Lösung der partiellen Differentialgleichung = 0. , 1848 .

[150]  Peter M. Topping,et al.  Reverse Bubbling and Nonuniqueness in the Harmonic Map Flow , 2002 .

[151]  H. Urakawa.  Calculus of variations and harmonic maps , 1993 .

[152]  Jürgen Jost,et al.  On the existence of harmonic diffeomorphisms between surfaces , 1982 .

[153]  Gang Tian,et al.  Energy identity for a class of approximate harmonic maps from surfaces , 1995 .

[154]  Ding Weiyue,et al.  Lusternik-Schnirelmann theory for harmonic maps , 1986 .

[155]  Fanghua Lin,et al.  Topology of sobolev mappings, II , 2003 .

[156]  Rugang Ye,et al.  Finite-time blow-up of the heat flow of harmonic maps from surfaces , 1992 .

[157]  P. Hajłasz.  Approximation of Sobolev mappings , 1994 .

[158]  F. Béthuel,et al.  A characterization of maps in $H^1 (B^3, S^2)$ which can be approximated by smooth maps , 1990 .

[159]  J. Qing.  The Dirichlet Problem for Harmonic Maps from the Disc into Kahler Manifolds , 1993 .

[160]  F. Béthuel,et al.  The approximation problem for Sobolev maps between two manifolds , 1991 .

[161]  Yuanlong Xin,et al.  Geometry of Harmonic Maps , 1996 .

[162]  N Kapouleas,et al.  Constant mean curvature surfaces constructed by fusing Wente tori , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[163]  Wei Yei Ding,et al.  Symmetric harmonic maps between spheres , 1988 .

[164]  F. Béthuel,et al.  Extensions for Sobolev mappings between manifolds , 1995 .

[165]  Nicolaos Kapouleas,et al.  Constant mean curvature surfaces in Euclidean three-space , 1987 .

[166]  F. Lin,et al.  Mappings minimizing the Lp norm of the gradient , 1987 .

[167]  V. Benci,et al.  The Dirichlet Problem for Harmonic Maps from the Disk into the Euclidean n-Sphere. , 1985 .

[168]  A. Freire,et al.  Uniqueness for the harmonic map flow in two dimensions , 1995 .

[169]  Michael Struwe,et al.  Existence and partial regularity results for the heat flow for harmonic maps , 1989 .

[170]  H. Bateman,et al.  The Solution of Partial Differential Equations by Means of Definite Integrals , 1904 .

[171]  I. McIntosh.  TWO REMARKS ON THE CONSTRUCTION OF HARMONIC TORI IN CPn , 1996 .

[172]  Jean-Michel Coron,et al.  Relaxed Energies for Harmonic Maps , 1990 .

[173]  O. Perron,et al.  Eine neue Behandlung der ersten Randwertaufgabe fürΔu=0 , 1923 .

[174]  Brian White,et al.  Homotopy classes in Sobolev spaces and energy minimizing maps , 1985 .

[175]  Fengbo Hang.  On the weak limits of smooth maps for the Dirichlet energy between manifolds , 2005, math/0611581.

[176]  Jürgen Jost,et al.  A maximum principle for harmonic mappings which solve a Dirichlet problem , 1982 .

[177]  ON THE EXISTENCE OF HARMONIC MORPHISMS FROM CERTAIN SYMMETRIC SPACES , 2006, math/0603297.

[178]  Hermann Weyl,et al.  The method of orthogonal projection in potential theory , 1940 .

[179]  Charles B. Morrey,et al.  The Problem of Plateau on a Riemannian Manifold , 1948 .

[180]  Karen Uhlenbeck,et al.  A regularity theory for harmonic maps , 1982 .