Isoperimetric inequality under Kähler Ricci flow

2012/03/07 by Gang Tian, Qi S. Zhang, Tian, Gang +1 · 1 citation
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.1203.1400

openalex publication_date 2012/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (\M, g(t)) be a Kähler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on (\M, g(t)), and a Poincaré inequality without assuming the Ricci curvature is bounded from below.

Citations

• Convergence of a Kähler-Ricci flow
• Differential equations on riemannian manifolds and their geometric applications

Cited by

• Laplace comparison on Kähler Ricci flow and convergence

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