Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type

2015/05/05 by Gang Tian, Tian, Gang, Zhenlei Zhang +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1505.01038

openalex publication_date 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the L⁴-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n≤ 3, any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of M in the Cheeger-Gromov topology.

Citations

• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

Cited by

• Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
• Fano Fibrations and Twisted Kähler-Einstein Metrics I
• Green's function estimates for compact Kähler manifolds and applications
• Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

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