Almost rigidity of convex hypersurfaces via the extinction time of mean curvature flow
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 877-884
https://doi.org/10.4134/BKMS.b200594
Published online June 3, 2021
Printed July 31, 2021
Xian-Tao Huang
Sun Yat-sen University
Abstract : 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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