166 research outputs found
The extension and convergence of mean curvature flow in higher codimension
In this paper, we first investigate the integral curvature condition to
extend the mean curvature flow of submanifolds in a Riemannian manifold with
codimension , 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
under suitable integral curvature conditions.Comment: 29 page
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