Pseudo-locality for a coupled Ricci flow

Abstract

Let $(M,g,\ddot{I}•)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $\ddot{I}•$. We show that a complete, $\hat{I}º$-noncollapsed solution $(M,g,\ddot{I}•)$ to this coupled Ricci flow with a Type I singularity at time $T<\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow.

references added, typos corrected