Mean curvature flow of higher codimension in Riemannian manifolds
Differential Geometry
2012-04-03 v1
Abstract
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching condition, then along the mean curvature flow the submanifold contracts smoothly to a round point in finite time. As a consequence we obtain a differentiable sphere theorem for submanifolds in a Riemannian manifold.
Keywords
Cite
@article{arxiv.1204.0107,
title = {Mean curvature flow of higher codimension in Riemannian manifolds},
author = {Kefeng Liu and Hongwei Xu and Entao Zhao},
journal= {arXiv preprint arXiv:1204.0107},
year = {2012}
}
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28 pages