Pseudolocality for the Ricci flow and applications
摘要
In \cite{P1}, Perelman established a differential Li-Yau-Hamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds (also see \cite{N2}). As an application of the LYH inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these results in the case of a complete non-compact Riemannian manifold. Using these results we prove that under certain conditions, a finite time singularity of the Ricci flow must form within a compact set. We also prove a long time existence result for the \KRF flow on complete non-negatively curved \K manifolds.
引用
@article{arxiv.math/0701153,
title = {Pseudolocality for the Ricci flow and applications},
author = {Albert Chau and Luen-Fai Tam and Chengjie Yu},
journal= {arXiv preprint arXiv:math/0701153},
year = {2007}
}
备注
44 pages; added Corollary to Theorem 1.1; correction to Theorem 8.1