A pseudolocality theorem for Ricci flow

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 $g_k(0)$.

11 pages, I have add one mild assumption on the theorem and completely rewrites the proof of the theorem which avoids the use of the logarithmic Sobolev inequality completely. I also obtain an extension of the compactness result of Hamilton on a sequence of complete pointed Riemannian manifolds evolving under Ricci flow

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Pseudolocality for the Ricci flow and applications
• Classification of compact ancient solutions to the Ricci flow on surfaces
• Uniqueness of solutions of Ricci flow on complete noncompact manifolds