The extension and convergence of mean curvature flow in higher codimension

Liu, Kefeng; Xu, Hongwei; Ye, Fei; Zhao, Entao

doi:10.1090/tran/7281

The extension and convergence of mean curvature flow in higher codimension
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by Kefeng Liu, Hongwei Xu, Fei Ye and Entao Zhao PDF

Trans. Amer. Math. Soc. 370 (2018), 2231-2262 Request permission

Abstract:

In this paper, we investigate the convergence of the mean curvature flow of closed submanifolds in $\mathbb {R}^{n+q}$. We show that if the initial submanifold satisfies some suitable integral curvature conditions, then along the mean curvature flow it will shrink to a round point in finite time.

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