報 告 人：史宇光 教授

報告題目：Positive mass theorem on singular spaces and some applications

報告時間：2025年6月25日（周三）上午09:00-10:00

報告地點：泉山校區5號樓107

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

            史宇光教授現為北京大學教授和博士生導師, 2005年入選年教育部新世紀優秀人才支持計劃；2007年獲得國家杰出青年科學基金項目資助；因在完備非緊Riemann流形幾何的研究中做出了杰出貢獻，以及在中國從事數學教學和研究中的重要貢獻，于2010年獲得Ramanujan獎；2016年入選第二批國家高層次人才特殊支持計劃科技創新領軍人才。相關研究成果發表于J. Differential Geom., Adv. Math.，Trans. Amer. Math. Soc., Comm. Anal. Geom.等權威數學期刊。

報告摘要：

               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.