Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold

2011/07/20 by Gang Tian, Tian, Gang, Shijin Zhang +5 · 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.1107.4018

openalex publication_date 2011/07/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the method in [TZhu5] to study the energy level L(⋅) of Perelman's entropy λ(⋅) for Kähler-Ricci flow on a Fano manifold. Consequently, we first compute the supremum of λ(⋅) in Kähler class 2πc₁(M) under an assumption that the modified Mabuchi's K-energy μ(⋅) defined in [TZhu2] is bounded from below. Secondly, we give an alternative proof to the main theorem about the convergence of Kähler-Ricci flow in [TZhu3].

Citations

• Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature Kähler metrics

Cited by

• Regularity of Kähler-Ricci flow
• Ricci flow and birational surgery
• Regularity of Kähler-Ricci flows on Fano manifolds
• The total second variation of Perelman's W-functional

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