A local curvature estimate for the Ricci-harmonic flow on complete Riemannian manifolds

2021/12/05 by Yi Li, Li, Yi, Miaosen Zhang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.02576

openalex publication_date 2021/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the local L^p estimate of Riemannian curvature for the Ricci-harmonic flow or List's flow introduced by List \citeList2005 on complete noncompact manifolds. As an application, under the assumption that the flow exists on a finite time interval [0,T) and the Ricci curvature is uniformly bounded, we prove that the L^p norm of Riemannian curvature is bounded, and then, applying the De Giorgi-Nash-Moser iteration method, obtain the local boundedness of Riemannian curvature and consequently the flow can be continuously extended past T.

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• A local curvature estimate for the Ricci flow
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• Curvature Estimates for the Ricci Flow II
• Integral curvature estimates for solutions to Ricci flow with L^p bounded scalar curvature