Positively Curved Complete Noncompact Kähler Manifolds

2002/11/24 by Bing-Long Chen, Chen, Bing-Long, Xi-Ping Zhu +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0211373

33 pages

arxiv created 2002/11/24 · openalex publication_date 2002/11/24 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. We prove that a complete noncompact Kähler surface with positive and bounded sectional curvature and with finite analytic Chern number c₁(M)² is biholomorphic to \C².

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