題  目：Isoparametric Submanifolds and Mean Curvature Flow

内容簡介：Ancient solutions are important in studying singularities of mean curvature flows (MCF). So far most rigidity results about ancient solutions are modeled on shrinking spheres or spherical caps. In this talk, I will describe the behavior of MCF for a class of submanifolds, called isoparametric submanifolds, which have more complicated topological type. We can show that all such solutions are in fact ancient solutions, i.e. they exist for all time which goes to negative infinity. Similar results also hold for MCF of regular leaves of polar foliations in simply connected symmetric spaces with non-negative curvature. I will also describe our conjectures proposed together with Terng on rigidity of ancient solutions to MCF for hypersurfaces in spheres. These conjectures are closely related to Chern’s conjecture for minimal hypersurfaces in spheres. This talk is based on joint works with Chuu-Lian Terng and Marco Radeschi.

報告人：北京大學  劉小博  教授

報告人簡介：本科畢業于清華大學，博士畢業于美國賓夕法尼亞大學，曾任美國聖母大學教授，現為北京大學講席教授。他曾在《Annals of Math.》、《Journal of  Differential Geometry》、《Duke Math. Journal》等國際一流期刊上發表多篇論文。由于在幾何與數學物理領域傑出的學術成就，他曾獲得美國 Sloan 研究獎，并應邀在 2006 年的國際數學家大會上做 45 分鐘報告。目前，他正擔任北京國際數學中心的副主任。

時  間：2021年6月11日（周五）上午10：30開始

地  點：騰訊在線會議  ID：908 965 709

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