On the Ricci curvature of Kahler-Ricci Flow

2021/11/24 by Cheuk Yan Fung, Fung, Cheuk Yan
Mathematics · #53E30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2111.12415

openalex publication_date 2021/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider n-dimensional compact Kahler manifold with semi-ample canonical line bundle under the long time solution of Kahler Ricci Flow. In particular, if the Kodaira dimension is one, Ricci curvature converge to negative of generalized Kahler Einstein metric ω_B locally away from singular set in C⁰_loc(ω(t)) topology.

Related

• Higher-Order Estimates of Long-Time Solutions to the Kähler-Ricci Flow
• Local curvature estimates of long-time solutions to the Kähler-Ricci flow
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
• Convergence of scalar curvature of Kahler-Ricci flow on manifolds of positive Kodaira dimension