Topic：Brown-York mass and compact manifolds with quasi-positive boundarydata

Reporter：Prof. TAM Luen Fai, from Chinese University of Hongkong
Date: December 5, 2019
Time: 4:00pm
Venue: Room 204, Nanhai Building

Abstract：In this talk, we will discuss the geometry of a compact threemanifold (Ω,g) with boundary and with nonnegative scalarcurvature.A previous result by Shi and Tam says that if the each boundarycomponent Σ of the boundary ofΩ has positive mean curvatureand positive Gaussian curvature, then the total mean curvature ofΣis no greater than the total mean curvature of Σwhen it isisometrically embedded in the Euclidean three space. This is equivalent tosay that the Brown-York mass of ΣinΩis nonnegative.Moreover, if the Brown-York mass is zero, then Ωis isometric toadomain in the Euclidean three space.In this talk, we will discuss the situation that the mean curvature ofΣis nonnegative and the Gaussian curvature of Σisnonnegative and is positive somewhere.This is a recent joint work with Yuguang Shi.