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arXiv · 1204.0107

Mean curvature flow of higher codimension in Riemannian manifolds

Kefeng Liu·Hongwei Xu·Entao Zhao
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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.

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Kefeng Liu, Hongwei Xu, Entao Zhao. 2012-03-31. Mean curvature flow of higher codimension in Riemannian manifolds. https://arxiv.org/abs/1204.0107

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