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Bull. Korean Math. Soc. 2021; 58(4): 877-884

Online first article June 3, 2021      Printed July 31, 2021

https://doi.org/10.4134/BKMS.b200594

Copyright © The Korean Mathematical Society.

Almost rigidity of convex hypersurfaces via the extinction time of mean curvature flow

Xian-Tao Huang

Sun Yat-sen University

Abstract

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We prove that if a compact convex hypersurface of $\mathbb{R}^{n+1}$ has almost maximal extinction time when it is evolved by the mean curvature flow, then it must be nearly round in the $C^{0}$-norm.

Keywords: Convex hypersurface, mean curvature flow, almost rigidity

MSC numbers: 53C44

Supported by: The author is partially supported by NSFC (Nos. 11701580 and 11521101) and Guangdong Natural Science Foundation 2019A1515011804.

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