Ricci-Deturck flow from rough metrics and applications

Abstract

Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and have small local scaling invariant gradient concentration. As applications, we use it to study several stability problems related to the scalar curvature.

36 pages, printing mistakes corrected, added result on positive mass Theorem on singular metrics