On diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature

2025/12/15 by Jianchun Chu, Man-Chun Lee, Chu, Jianchun +3
Mathematics · #32Q10 #53C24 (Secondary) #53C55 (Primary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2512.13097

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish some diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature.

Citations

• Laplacian comparison theorems on complete Kähler manifolds and applications
• First eigenvalue estimates on complete Kähler manifolds
• On Kähler manifolds with non-negative mixed curvature
• Conjugate radius, volume comparison and rigidity
• The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
• Diameter rigidity for Kahler manifolds with positive bisectional curvature
• Comparison geometry of holomorphic bisectional curvature for Kaehler manifolds and limit spaces
• On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature (with an appendix by Yuchen Liu)

Related

• Diameter rigidity for Kahler manifolds with positive bisectional curvature
• Diameter Rigidity for Kähler manifolds with positive bisectional curvature
• Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound
• Conjugate radius, volume comparison and rigidity
• The rigidity of dimension estimate for holomorphic functions on Kähler manifolds