报 告 人：史宇光 教授
报告题目：Positive mass theorem on singular spaces and some applications
报告时间：2025年6月25日（周三）上午09:00-10:00
报告地点：泉山校区5号楼107
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
史宇光教授现为北京大学教授和博士生导师, 2005年入选年教育部新世纪优秀人才支持计划；2007年获得国家杰出青年科学基金项目资助；因在完备非紧Riemann流形几何的研究中做出了杰出贡献，以及在中国从事数学教学和研究中的重要贡献，于2010年获得Ramanujan奖；2016年入选第二批国家高层次人才特殊支持计划科技创新领军人才。相关研究成果发表于J. Differential Geom., Adv. Math.，Trans. Amer. Math. Soc., Comm. Anal. Geom.等权威数学期刊。
报告摘要：
In this talk, I will discuss some positive mass theorems for certain singularspaces 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 asymptotic flat (AF) manifolds with arbitrary ends, non-negative scalar curvature and dimension less than or equal to 8. This also leads to positive mass theorem of 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-dimensianal manifold with generic metrics.This talk is based on my recent joint work with He Shiliang and Prof. Yu Haobin.