On complete noncompact Kähler manifolds with positive bisectional curvature
By Binglong Chen, Xiping Zhu. 2002
65 citations recorded by the source corpus.
Abstract.We prove that a complete noncompact Kähler manifold Mnof positive bisectional curvature satisfying suitable growth conditions is biholomorphic to a pseudoconvex domain of Cn and we show that the manifold is topologically R2n. In particular, when Mn is a Kähler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to C2.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/62b3a7121d43c2fe48f3dacded242208db466dc1
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Recent Progress on Ricci Solitons (2009, result): “In the Kähler case, the same result as Theorem 5.1 (assuming nonnegative curvature operator) is obtained independently by Chen-Zhu [27].”
- Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature (2005, background): “Now it has been found to be a powerful tool to understand the geometry, topology and complex structure of manifolds (see for example [11], [12], [13], [17], [18], [3], [20], [8], [7], [26], [27] etc.”
- Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature (2003, methodology): “implies (6.4) and (6.13) are true uniformly for all o ∈ M (with ||ρ|| replaced by R). Later, using K¨ ahler-Ricci flow of [39], it was generalized in [ 6 ] by only assuming that (6.13) holds uniformly for all o ∈ M .I n order to use the K¨ ahler Ricci flow, it was also assumed that R is bounded in [”
- A Uniformization Theorem Of Complete Noncompact K\"{a}hler Surfaces With Positive Bisectional Curvature (2002, unknown): “(6.19) By (6.1), (2.7) and the standard volume comparison, we have ∫ M R2ϕdx ≤ ( sup M R ) ∫ M R(x)e − ( 1+ d(x,x0) r ) dx ≤ ( sup M R ) · (∫ B(x0,r) R(x)dx+ ∞∑ k=0 e−2 k−1 ∫ B(x0,2k+1r)\B(x0,2kr) R(x)dx ) ≤ C17r2 log (2 + r) (6.20) and ∫ M ϕdx ≤ ∫ M e − ( 1+ d(x,x0) r ) dx ≤ ∫ B(x0,r)…”