Abstract: 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 the half-space. As application, we give a new proof of Wente’s Alexandrov-type theorem for embedded CMC capillary hypersurfaces. Moreover, the proof can be adapted to the anisotropic case, which enable us to prove an Alexandrov-type theorem for embedded anisotropic capillary hypersurfaces. This is based on joint works with Xiaohan Jia, Guofang Wang and Xuwen Zhang.

Speaker: Chao Xia is currently a professor at Xiamen University. He obtained his PhD degree at University of Freiburg in 2012. His research focuses on differential geometry and geometric analysis.