Geometric Analyisis Seminar: Quermassintegral preserving curvature flows in the sphere

：Julian Scheuer（德国法兰克福大学）
：2022-12-01 15:30
：腾讯会议ID：216-291-595（无密码）

报告人：Julian Scheuer（德国法兰克福大学）

时  间：12月01日下午15:30-17:00

地  点：腾讯会议ID：216-291-595（无密码）

内容摘要:

It is known since the seminal work by Huisken on the volume preserving mean curvature flow (VPMCF) from 1987, that the VPMCF for hypersurfaces of the sphere may lose convexity and hence a study of this flow has been avoided so far. The same problem arises for every nonlocal flow which preserves any of the other quermassintegrals. Without the presence of a global term, Guan and Li have constructed a flow within the sphere, which preserves the volume and converges smoothly to a geodesic sphere. However, the corresponding quermassintegral preserving versions of this flow are not understood until today, because it seems impossible to prove curvature estimates. In this talk, we introduce a quermassintegral preserving flow for hypersurfaces of the sphere, which is constrained by a global and a local term. This flow is shown to converge to a geodesic sphere and hence provides the first such example of a quermassintegral preserving curvature flow in the sphere, for which one can obtain smooth estimates. This is joint work with Esther Cabezas-Rivas.

个人简介：

Julian Scheuer，德国法兰克福大学教授。2013年于德国海德堡大学获得博士学位。之后在海德堡大学、弗莱堡大学做博士后研究工作，曾任英国卡迪夫大学讲师。他的研究领域主要是几何进化方程，特别是曲率流方程的理论分析与应用，在Adv.Math.,Math.Ann.,Crelle,JDG,CMP,TAMS,IMRN,JFA,CVPDE,CPDE,APDE等数学刊物发表论文30余篇。

 

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