A pseudolocality theorem for Ricci flow

TL;DR

This paper provides a simplified proof of a pseudolocality theorem for Ricci flow, extending Hamilton's compactness result for sequences of manifolds with bounded curvature and positive injectivity radius.

Contribution

It offers a new, simpler proof of a pseudolocality theorem for Ricci flow and extends Hamilton's compactness theorem without relying on Perelman's pseudolocality theorem.

Findings

Simplified proof of pseudolocality for Ricci flow

Extension of Hamilton's compactness theorem

No use of Perelman's pseudolocality theorem

Abstract

In this paper we will give a simple proof of a modification of a result on pseudolocality for the Ricci flow by P.Lu without using the pseudolocality theorem 10.1 of Perelman [P1]. We also obtain an extension of a result of Hamilton on the compactness of a sequence of complete pointed Riemannian manifolds $\{(M_k,g_k(t),x_k)\}_{k=1}^{\infty}$ evolving under Ricci flow with uniform bounded sectional curvatures on $[0,T]$ and uniform positive lower bound on the injectivity radii at $x_k$ with respect to the metric $g_k(0)$.