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Removable singularity of positive mass theorem with continuous metrics

主 讲 人 :盛为民    教授

活动时间:08月27日16时00分    

地      点 :云顶国际平台网站腾讯会议 ID:317 576 247,会议密码:202108

讲座内容:

In this talk, I will introduce my recent work withWenshuai Jiang and  Huaiyu Zhang. Weconsider asymptotically flat Riemannian manifolds endowed with a continuousmetric and the metric is smooth away from a compact subset with certainconditions. If the metric is Lipschitz and the scalar curvature is nonnegativeaway from a closed subset with $(n-1)$-dimensional Hausdorff measure zero,  we show that the ADM mass of each end isnonnegative. Furthermore, if the ADM mass of some end is zero, then we showthat the manifold is isometric to the Euclidean space. The Hausdorff measurecondition is optimal, which confirms a conjecture of Lee in 2013. The argumentof the nonnegativity is based a smoothing argument with some new estimates suchas a $L^1$-scalar curvature approximation estimates. The proof of the rigidityrelies on the RCD theory where we show that the manifold has nonnegative Riccicurvature in RCD sense.

主讲人介绍:

盛为民,浙江大学数学科学学院教授、副院长。美国数学会会员,美国数学评论评论员。主要研究兴趣在于具有一定几何或物理背景的微分几何和偏微分方程,包括预定曲率问题,k-Yamabe问题,以及曲率流问题。

发布时间:2021-08-25 15:38:46

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