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研讨班

09-04-2021

几何分析研讨班第22期-Removable singularity of positive mass theorem with continuous metrics-盛为民教授(浙江大学)

报告题目:Removable singularity of positive mass theorem with continuous metrics

报告人:盛为民教授(浙江大学)

报告时间:2021年04月12日周一10:00-11:00

腾讯会议ID:895 3600 0097

摘要:In this talk, I will introduce my recent work on Positive Mass Theorem which is a joint work with Wenshuai Jiang and Huaiyu Zhang. We consider asymptotically flat Riemannian manifolds endowed with a continuous metric and the metric is smooth away from a compact subset with certain conditions. If the metric is Lipschitz and the scalar curvature is nonnegative away from a closed subset with $(n-1)$-dimensional Hausdorff measure zero, then we show that the ADM mass of each end is nonnegative. Furthermore, if the ADM mass of some end is zero, then we prove that the manifold is isometric to the Euclidean space. The Hausdorff measure condition is optimal, which confirms a conjecture of Lee in 2013. The proof of the nonnegativity is based a smoothing argument with some new estimates such as a $L^1$-scalar curvature approximation estimates. The proof of the rigidity relies on the RCD theory where we show that the manifold has nonnegative Ricci curvature in RCD sense. The idea involving RCD theory in the proof turns out to be much more suitable in the study of the rigidity for continuous metrics. Furthermore, our result generalizes the result of Lee-LeFloch(2015) from spin to non-spin.

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