Tuesday February 11th, 2025 | |
| Time: | 4:00 PM - 5:15 PM |
| Title: | Smoothing $L^∞$ Riemannian metrics with nonnegative scalar curvature outside of a singular set |
| Speaker: | Paula Burkhardt-Guim, Stony Brook University |
| Location: | P-131 |
| Abstract: | |
| Abstract: We show that any $L^∞$ Riemannian metric $g$ on $R^n$ that is smooth with nonnegative scalar curvature away from a singular set of finite $(n-α)$-dimensional Minkowski content, for some $α>2$, admits an approximation by smooth Riemannian metrics with nonnegative scalar curvature, provided that $g$ is sufficiently close in $L^∞$ to the Euclidean metric. The approximation is given by time slices of the Ricci-DeTurck flow, which converge locally in $C^∞$ to $g$ away from the singular set. We also identify conditions under which a smooth Ricci-DeTurck flow starting from a $L^∞$ metric that is uniformly bilipschitz to Euclidean space and smooth with nonnegative scalar curvature away from a finite set of points must have nonnegative scalar curvature for positive times. | |