Local derivative estimates for the heat equation coupled to the Ricci flow
arXiv:1812.10296
Abstract
In this note we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang's work, we extend some results of Zhang and Bamler-Zhang including distance distortion estimates and a backward pseudolocality theorem for Ricci flow on compact manifolds to the noncompact case.
31 pages, added an appendix; to appear in Communications in Contemporary Mathematics