發表時間:2020-12-23 閱讀次數:1758次
報告題目: 杰出學者講壇(五十九):Isoparametric Submanifolds and Mean Curvature Flow
報 告 人:劉小博 教授
報告人所在單位:北京大學
報告日期:2020-12-23 星期三
報告時間:16:00-17:00
報告地點:光華東主樓2201
  
報告摘要:

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. We also proposed conjectures about 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.

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本年度學院報告總序號:13

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