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arXiv · 1104.0971

The extension and convergence of mean curvature flow in higher codimension

Kefeng Liu·Hongwei Xu·Fei Ye·Entao Zhao
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Abstract

In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow of hypersurfaces due to Le-\v{S}e\v{s}um \cite{LS} and the authors \cite{XYZ1,XYZ2}. Using the extension theorem, we prove two convergence theorems for the mean curvature flow of closed submanifolds in ${R}^{n+d}$ under suitable integral curvature conditions.

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Kefeng Liu, Hongwei Xu, Fei Ye, Entao Zhao. 2011-04-05. The extension and convergence of mean curvature flow in higher codimension. https://arxiv.org/abs/1104.0971

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