報(bào) 告 人：史宇光 教授

報(bào)告題目：Positive mass theorem on singular spaces and some applications

報(bào)告時(shí)間：2025年6月25日（周三）上午09:00-10:00

報(bào)告地點(diǎn)：泉山校區(qū)5號(hào)樓107

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

            史宇光教授現(xiàn)為北京大學(xué)教授和博士生導(dǎo)師, 2005年入選年教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃；2007年獲得國(guó)家杰出青年科學(xué)基金項(xiàng)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(xiàn)，以及在中國(guó)從事數(shù)學(xué)教學(xué)和研究中的重要貢獻(xiàn)，于2010年獲得Ramanujan獎(jiǎng)；2016年入選第二批國(guó)家高層次人才特殊支持計(jì)劃科技創(chuàng)新領(lǐng)軍人才。相關(guān)研究成果發(fā)表于J. Differential Geom., Adv. Math.，Trans. Amer. Math. Soc., Comm. Anal. Geom.等權(quán)威數(shù)學(xué)期刊。

報(bào)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.