Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied by the authors in [LT]. In this paper, we will show that all these solutions are ancient solutions. We also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the Chern's conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres.

中文翻译：

---

等参子流形的平均曲率流的古老解

作者在 [LT] 中研究了欧几里德空间和球体中等参子流形的平均曲率流。在本文中，我们将证明所有这些解决方案都是古老的解决方案。我们还讨论了球体中超曲面的古代平均曲率流的刚性及其与关于球体中最小超曲面的第二基本形式的范数的陈猜想的关系。