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 (J Differ Geom 82(2):363–382, 2009).