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, the 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 will briefly review the positive mass theorem due to Schoen-Yau-Witten and Brown-York mass theorem due to Shi-Tam. As applications of Shi-Tam's result, we show how to use it to derive some interesting geometric results such as esitmates of first eigenvalue of Laplacian with scalar curvature positively lower bounded and an area estimate of critical set for Besse's conjecture etc.

主持人：焦翔宇 副教授