数学研究所
学术报告
几何拓扑研讨班
Speaker: 史宇光 教授（北京大学）
Inviter: 王健 副研究员
Language: Chinese
Title: Positive mass theorems on singular spaces and some applications
Time&Venue: 2025年4月9日（星期三） 10:30-11:30 & 晨兴410
Abstract: In this talk, I will discuss some positive mass theorems for certain singular spaces inspired by the dimension reduction techniques employed in the study of the geometry of manifolds with positive scalar curvature. In these results, we assume only that the scalar curvature is non-negative in a strong spectral sense, which aligns well with the stability condition of a minimal hypersurface in an ambient manifold with non-negative scalar curvature. As an application, we provide a characterization of asymptotically flat (AF) manifolds with arbitrary ends, non-negative scalar curvature, and dimension less than or equal to 8.This also leads to positive mass theorems for AF manifolds with arbitrary ends and dimension less than or equal to 8 without using N.Smale's regularity theorem for minimal hypersurfaces in a compact 8-dimensional manifold with generic metrics. The talk is based on my recent joint work with He Shihang and Yu Haobin.
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