Differential Geometry Seminar: Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow

Seminar | September 9 | 3-4 p.m. | 939 Evans Hall

 Paula Burkhardt-Guim, UC Berkeley

 Department of Mathematics

We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from $C^0$ initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from $C^0$ initial data.