报告题目 (Title)：Positive mass theorem with low-regularity Riemannian metrics
报告人 (Speaker)：盛为民 教授（浙江大学）
报告时间 (Time)：2022年5月11日(周三) 10:00-11:00
报告地点 (Place)：腾讯会议（716-8675-1741）
邀请人(Inviter)：席东盟、李晋、张德凯
主办部门：理学院数学系
报告摘要：In this talk, I would like to introduce our recent results with W. Jiang and H. Zhang on positive mass theorem and scalar curvature lower bounds with low-regularity Riemannian metrics. We first consider asymptotically flat Riemannian manifolds endowed with a continuous metric and the metric is smooth away from a compact subset with certain conditions. I will show the positive mass theorem is true if the metric is Lipschitz and the scalar curvature is nonnegative away from a closed subset with $(n-1)$-dimensional Hausdorff measure zero. On compact manifolds with a continuous initial metric, I will show the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in distributional sense. As an application, we use this result to study the relation between Yamabe invariant and Ricci flat metrics.
