Appears in collection : Not Only Scalar Curvature Seminar

In this talk, we will discuss the existence theory of Ricci-DeTurck flow when the initial metric is not smooth. This can be viewed as the Ricci Flow with a fixed gauge. As a application, we will discuss how we can use the geometric flow to study rigidity problems in scalar curvature when the metric is not entirely smooth. This is based on joint works with Chu, Tam and Huang.