The conical Kähler-Ricci flow on Fano manifolds

2014/02/08 by Jiawei Liu, Xi Zhang, Liu, Jiawei +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1402.1832

openalex publication_date 2014/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the long-term behavior of the conical Kähler-Ricci flow on Fano manifold M. First, based on our work of locally uniform regularity for the twisted Kähler-Ricci flows, we obtain a long-time solution to the conical Kähler-Ricci flow by limiting a sequence of these twisted flows. Second, we study the uniform Perelman's estimates of the twisted Kähler-Ricci flows. After that, we prove that the conical Kähler-Ricci flow must converge to a conical Kähler-Einstein metric if there exists one.

Citations

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Conical Kahler-Einstein metric revisited

Cited by

• The conical Kähler-Ricci flow with weak initial data on Fano manifold
• Stability of the conical Kähler-Ricci flows on Fano manifolds

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