Pseudolocality and uniqueness of Ricci flow on almost Euclidean noncompact manifolds

TL;DR

This paper establishes a pseudolocality theorem for certain noncompact Ricci flows, leading to a strong uniqueness result on Euclidean space, thus addressing a question by B-L. Chen.

Contribution

It introduces a pseudolocality theorem for $\\mathcal{L}$-complete noncompact Ricci flows without bounded curvature, and proves strong uniqueness on Euclidean space.

Findings

Proved pseudolocality theorem for $\\mathcal{L}$-complete noncompact Ricci flows.

Established strong uniqueness of Ricci flow on Euclidean space.

Partially answered B-L. Chen's question on Ricci flow uniqueness.

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.