Ancient solutions of codimension two surfaces with curvature pinching in $\mathbb{R}^4$
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 1049-1060
Published online July 31, 2020
Zhengchao Ji
Zhejiang University
Abstract : 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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