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

Yi Li; Miaosen Zhang

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arXiv · 2112.02576

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

Yi Li·Miaosen Zhang

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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 \cite{List2005} 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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Yi Li, Miaosen Zhang. 2021-12-05. A local curvature estimate for the Ricci-harmonic flow on complete Riemannian manifolds. https://arxiv.org/abs/2112.02576

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