The extension and convergence of mean curvature flow in higher codimension

Details The extension and convergence of mean curvature flow in higher codimension The extension and convergence of mean curvature flow in higher codimension

2011-04-05

arxiv.org/abs/1104.0971v1

Mathematics

Differential Geometry

29 pages

Scientific paper

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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