Non-negatively curved Kähler manifolds with average quadratic curvature decay

2005/10/12 by Albert Chau, Chau, Albert, Luen-Fai Tam +1
Mathematics · #35K90 #53C55 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:35K90 #msc:53C55

paper · pdf · doi:10.48550/arxiv.math/0510252

arxiv created 2005/10/12 · openalex publication_date 2005/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M, g) be a complete non-compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in \citeCT3, we prove that the universal cover \wt M of M is biholomorphic to \ceⁿ provided either that (M, g) has average quadratic curvature decay, or M supports an eternal solution to the Kähler-Ricci flow with non-negative and uniformly bounded holomorphic bisectional curvature. We also classify certain local limits arising from the Kähler-Ricci flow in the absence of uniform estimates on the injectivity radius.

Citations

• A Compactness Property for Solutions of the Ricci Flow

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