Pseudolocality for the Ricci Flow and Applications

Chau, Albert ; Tam, Luen-Fai ; Yu, Chengjie

Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 55-85

Résumé

Perelman established a differential Li-Yau-Hamilton $\left( \text{LHY} \right)$ type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds. As an application of the $\text{LHY}$ 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 noncompact 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. The conditions are satisfied by asymptotically flatmanifolds. We also prove a long time existence result for the Kähler-Ricci flow on complete nonnegatively curved Kähler manifolds.

Détail

DOI : 10.4153/CJM-2010-076-2

Mots-clés : 53C44, 58J37, 35B35

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