Generalized Reilly\'s Formula and its Applications


14:00:00 - 16:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Alexandrov\'s theorem provides useful information about hypersurfaces in Euclidean space: Every compact embedded hypersurface of constant mean curvature in Euclidean space is a standard sphere.This theorem is proved by using Reilly\'s formula,which is an application of the integral version of Bochner\'s fomula and divergence theorem. In this talk, I will talk about a generalized version of Reilly\'s formula, which can also prove a generalized version of Alexandrov theorem: Every embedded closed hypersurface in the hemispehre of hyperbolic space with constant mean curvature is a geodesic sphere.
This talk is based on Guohuan Qiu and Chao Xia\'s paper.(arXiv:1405.4518v1[math.DG]18 May 2014)