Pseudolocality and uniqueness of Ricci flow on almost Euclidean noncompact manifolds

Abstract

In this paper, we prove a pseudolocality-type theorem for $\mathcal{L}$-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In particular, we prove the strong uniqueness theorem for the $\mathcal{L}$-complete Ricci flow on the Euclidean space. This partially answers a question proposed by B-L.~Chen.