Heintze-Karcher’s inequality and Alexandrov’s soap bubble theorem

讲座时间 Datetime: 2022年7月8日，星期五，10:00-11:00

地点 Venue: 腾讯线上会议：580-421-690

主持人 Host：魏国栋

报告人 Speaker: 夏超

单位 Affiliation: 厦门大学

报告摘要 Abstract:

Heintze-Karcher’s inequality is an interesting geometric inequality for embedded closed hypersurfaces, which can be used to prove Alexandrov’s soap bubble theorem on embedded closed CMC hypersurfaces. In this talk, we will introduce our recent work on Heintze-Karcher-type inequality for capillary hypersurfaces, via two different methods. As an application, we reprove Alexandrov’s theorem for hypersurfaces with capillary boundary in the half-space and the half-ball. Moreover, we prove new Alexandrov’s theorem and non-existence result for embedded CMC capillary surfaces in a wedge. This talk is based on ongoing joint work with Xiaohan Jia, Guofang Wang and Xuwen Zhang.