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.