Heintze-Karcher's inequality and Alexandrov’s soup bubble theorem for capillary hypersurfaces
报告人：夏超
报告地点：人民大街校区数学与统计学院二楼会议室
报告时间：2025年10月19日（星期日）16:00-17:00
邀请人：数学与统计学院
报告摘要：
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.
主讲人简介：
夏超，厦门大学数学科学学院院长、教授、博士生导师，福建省“闽江学者”特聘教授。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。曾入选国家高层次青年人才计划，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，论文发表在J. Differ. Geom. 、Math. Ann.、Peking Math. J.、Adv. Math.、 ARMA、TAMS、IMRN、CVPDE、CAG、JGA等国际重要数学期刊。
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