Bull. Korean Math. Soc. 2020; 57(4): 1049-1060
Online first article February 28, 2020 Printed July 31, 2020
https://doi.org/10.4134/BKMS.b190728
Copyright © The Korean Mathematical Society.
Zhengchao Ji
Zhejiang University
We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in \cite{RS} and we also remove the condition that the second fundamental form is uniformly bounded when $t\in(-\infty, -1)$.
Keywords: Mean curvature flow, ancient solutions, curvature pinching
MSC numbers: Primary 53C44, 35K55
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