Pseudolocality for the Ricci flow and applications
| dc.creator | Chau, Albert | |
| dc.creator | Tam, Luen-Fai | |
| dc.creator | Yu, Chengjie | |
| dc.date | 2007-01-05 | |
| dc.date | 2007-02-24 | |
| dc.date.accessioned | 2026-07-07T07:48:18Z | |
| dc.date.available | 2026-07-07T07:48:18Z | |
| dc.description | 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. | |
| dc.description | 44 pages; added Corollary to Theorem 1.1; correction to Theorem 8.1 | |
| dc.identifier | https://arxiv.org/abs/math/0701153 | |
| dc.identifier | http://arxiv.org/abs/math/0701153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124450 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C44 | |
| dc.title | Pseudolocality for the Ricci flow and applications | |
| dc.type | text |