Shu-Yu Hsu
Published 2009-08-06, updated 2010-10-06Version 3
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 $g_k(0)$.
Comments: 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
Ricci flows with unbounded curvature
Simple proofs of some results of Perelman on Ricci flow
Backwards uniqueness of the Ricci flow
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