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

主講人：夏超 廈門大學(xué)教授

時(shí)間：2024年4月1日10：30

地點(diǎn)：騰訊會(huì)議 726 445 118

舉辦單位：數(shù)理學(xué)院

主講人介紹：夏超，廈門大學(xué)教授、博士生導(dǎo)師，福建省“閩江學(xué)者”特聘教授。2007年四川大學(xué)本科畢業(yè)，2012年于德國(guó)弗萊堡大學(xué)獲博士學(xué)位，先后在德國(guó)馬克斯普朗克應(yīng)用數(shù)學(xué)研究所、加拿大麥吉爾大學(xué)做博士后研究。獲福建省青年科技獎(jiǎng)。主要研究領(lǐng)域是微分幾何與幾何分析，在超曲面幾何中的等周型不等式和相關(guān)剛性、幾何自由邊界問題、預(yù)定曲率和曲率流、特征值估計(jì)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等國(guó)際高水平數(shù)學(xué)期刊發(fā)表論文40余篇。

內(nèi)容介紹：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.