Heintze-Karcher's inequality and Alexandrov’s theorem for capillary hypersurfaces

主讲人：夏超 厦门大学教授

时间：2024年4月1日10：30

地点：腾讯会议 726 445 118

举办单位：数理学院

主讲人介绍：夏超，厦门大学教授、博士生导师，福建省“闽江学者”特聘教授。2007年四川大学本科毕业，2012年于德国弗莱堡大学获博士学位，先后在德国马克斯普朗克应用数学研究所、加拿大麦吉尔大学做博士后研究。获福建省青年科技奖。主要研究领域是微分几何与几何分析，在超曲面几何中的等周型不等式和相关刚性、几何自由边界问题、预定曲率和曲率流、特征值估计等方面取得了若干研究成果，已在J. Differ. Geom.、Math. Ann.、Adv. Math.、Peking Math. J.、ARMA、TAMS、IMRN、CVPDE、CAG、JGA等国际高水平数学期刊发表论文40余篇。

内容介绍：Heintze-Karcher’s inequality is an optimal geometric inequality for embedded closed hypersurfaces, which can be used to prove Alexandrov’s soap bubble theorem on embedded closed CMC hypersurfaces in the Euclidean space. In this talk, we introduce a Heintze-Karcher-type inequality for hypersurfaces with boundary in convex domains. As application, we give a new proof of Wente’s Alexandrov-type theorem for embedded CMC capillary hypersurfaces in the half-space. Moreover, the proof can be adapted to the anisotropic case in the convex cone, which enable us to prove Alexandrov-type theorem for embedded anisotropic capillary hypersurfaces in the convex cone. This is based on joint works with Xiaohan Jia, Guofang Wang and Xuwen Zhang.