The Ricci Flow on Complete Noncompact K\"{a}hler Manifolds

In this paper we survey the recent developments of the Ricci flows on complete noncompact K\"{a}hler manifolds and their applications in geometry.

[1]  Lei Ni,et al.  LIOUVILLE PROPERTIES OF PLURISUBHARMONIC FUNCTIONS , 2002, math/0212364.

[2]  Xiping Zhu,et al.  Volume Growth and Curvature Decay of Positively Curved K , 2002, math/0211374.

[3]  Xiping Zhu,et al.  A Uniformization Theorem Of Complete Noncompact K\"{a}hler Surfaces With Positive Bisectional Curvature , 2002, math/0211372.

[4]  Xiping Zhu,et al.  On complete noncompact Kähler manifolds with positive bisectional curvature , 2002, math/0211370.

[5]  Lei Ni,et al.  Kähler-Ricci Flow and the Poincaré-Lelong Equation , 2002, math/0211219.

[6]  B. Chow.  A Gradient Estimate for the Ricci–Kähler Flow , 2001 .

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

[8]  W. To.  Quasi-projective embeddings of noncompact complete Kähler manifolds of positive Ricci curvature and satisfying certain topological conditions , 1991 .

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

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

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

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

[13]  Y. Siu.  Pseudoconvexity and the problem of Levi , 1978 .

[14]  T. Mabuchi.  C 3-Actions and algebraic threefolds with ample tangent bundle , 1978, Nagoya Mathematical Journal.

[15]  R. Greene,et al.  C∞ convex functions and manifolds of positive curvature , 1976 .

[16]  C. P. Ramanujam.  A topological characterisation of the affine plane as an algebraic variety , 1971 .

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

[18]  Detlef Gromoll,et al.  The structure of complete manifolds of nonnegative curvature , 1968 .

[19]  Lei Ni.  Vanishing theorems on complete Kähler manifolds and their applications , 1998 .

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

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

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

[23]  Wan-Xiong Shi.  Ricci deformation of the metric on complete noncompact Kähler manifolds , 1990 .

[24]  Wan-Xiong Shi.  Deforming the metric on complete Riemannian manifolds , 1989 .

[25]  A. Nadel,et al.  Compactification of complete Kähler manifolds of negative Ricci curvature , 1988 .

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

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

[28]  E. Witten.  Holomorphic Morse Inequalities , 1984 .

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

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

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

[32]  C. Ferraris.  On manifolds with positive curvature , 1972 .