中科院数学与系统科学研究院

数学研究所

学术报告

微分几何研讨班

报告人： 朱锦天 博士（Peking University）

题  目：Researches on manifolds with scalar curvature bounded from below

时  间：2023.01.05（星期四），10:15-11:15

地  点：腾讯会议：768-127-358

摘  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.