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院士论坛、杰出学者讲坛、杰出校友讲坛|
发表时间:2020-12-23 阅读次数:1814次
报告题目: 杰出学者讲坛(五十九):Isoparametric Submanifolds and Mean Curvature Flow
报 告 人:刘小博 教授
报告人所在单位:北京大学
报告日期:2020-12-23 星期三
报告时间:16:00-17:00
报告地点:光华东主楼2201
  
报告摘要:

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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