Positive mass theorem with low-regularity Riemannian metrics

Weimin Sheng, Zhejiang University

*Please note the time change for this talk*

Online Talk

Zoom Link: https://princeton.zoom.us/j/99576580357

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.