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Quasi-local mass and uniqueness of isoperimetric surfaces in asymptotically hyperbolic manifolds

史宇光 教授(北京大学)
Tuesday, September 11th, 2018, 10:00 AM  闵行校区数学楼402
Abstract: Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary. It is interesting to see that some of quasi-local masses, like Brown-York mass, Hawking mass and isoperimetric mass have deep relation with classical isoperimetric inequality in asymptotically flat (hyperbolic) manifolds. In this talk, I will discuss these relations and finally give an application in the uniqueness of isoperimetric surfaces in asymptotically Ads-Schwarzschilds manifold with scalar curvature . This talk is based on my recent joint works with M.Echmair, O.Chodosh and my Ph.D student J. Zhu .
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