Pseudolocality for the Ricci Flow and Applications
نویسندگان
چکیده
In [26], Perelman established a differential Li-YauHamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds (also see [23]). 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 Kähler-Ricci flow flow on complete non-negatively curved Kähler manifolds.
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