中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：夏超 教授（厦门大学）
题 目：Heintze-Karcher's inequality and Alexandrov’s theorem for capillary hypersurfaces
时 间：2023.06.12（星期一）16:00-17:00
地 点：思源楼S813
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 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.
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