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arXiv · 1204.0106

Deforming submanifolds of arbitrary codimension in a sphere

Kefeng Liu·Hongwei Xu·Entao Zhao
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Abstract

In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere $\mathbb{S}^{n+d}$ under integral curvature conditions. As a consequence, we obtain several differentiable sphere theorems for certain submanifolds in $\mathbb{S}^{n+d}$.

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Kefeng Liu, Hongwei Xu, Entao Zhao. 2012-03-31. Deforming submanifolds of arbitrary codimension in a sphere. https://arxiv.org/abs/1204.0106

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