论文信息 - Positively Curved Complete Noncompact K\"{a}hler Manifolds

Positively Curved Complete Noncompact K\"{a}hler Manifolds

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. We prove that a complete noncompact K\"ahler surface with positive and bounded sectional curvature and with finite analytic Chern number $c_{1}(M)^{2}$ is biholomorphic to ${\C}^2$.

Xiping Zhu | Binglong Chen

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

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

[3] N. Mok. An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties , 1990 .

[4] R. Schoen,et al. Lp and mean value properties of subharmonic functions on Riemannian manifolds , 1984 .

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

[6] R. Simha. On the Analyticity of Certain Singularity Sets , 1975 .

[7] C. Fefferman. The Bergman kernel and biholomorphic mappings of pseudoconvex domains , 1974 .

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

[9] Alfred Huber,et al. On subharmonic functions and differential geometry in the large , 1958 .

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

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

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