Abstract: Positive mass theorem is one of the most fundamental results in both physics and mathematics. It has many applications in various fields of geometric analysis. As its compact manifold version, Shi-Tam's positive mass theorem for Brown-York mass has been also proved to be a very powerful tool in the study of geometry. In this talk, we first present some applications of Brown-York mass on problems involving scalar curvature, which includes an eigenvalue estimate for Laplacian on manifolds with boundary, an estimate of the area of horizons of vacuum static spaces with positive cosmological constant and a partial solution to Besse’s conjecture. In the end, we will briefly talk about a possible generalization of Brown-York mass for vacuum static spaces. This talk is main based on some joint works with Dr. Fang Yi in Anhui University of Technology and Prof. Qing Jie in UC Santa Cruz and Peking University.
