Researches on manifolds with scalar curvature bounded from below

2023.01.05（星期四），10:15-11:15

点：腾讯会议：768-127-358

要：The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems coming from these two fields. Roughly speaking, we are interested in mass-related problems from Mathematical General Relativity and the interplay between scalar curvature and topology/geometry from Riemannian Geometry. Later, I'll present some of my works along these directions including positive mass theorem with arbitrary ends/incompressible condition, uniqueness of isoperimetric surface in asymptotically Schwarzschild-ADS $3$-manifolds with positive mass, as well as the Gauss-Bonnet inequality. Finally, I'll talk about some potential directions in my further research.