Heat kernel bounds, ancient $κ$ solutions and the Poincaré conjecture
| dc.creator | Zhang, Qi S. | |
| dc.date | 2008-12-12 | |
| dc.date | 2009-02-21 | |
| dc.date.accessioned | 2026-07-07T12:44:24Z | |
| dc.date.available | 2026-07-07T12:44:24Z | |
| dc.description | We establish certain Gaussian type upper bound for the heat kernel of the conjugate heat equation associated with 3 dimensional ancient $κ$ solutions to the Ricci flow. As an application, using the $W$ entropy associated with the heat kernel, we give a different and shorter proof of Perelman's classification of backward limits of these ancient solutions. The current paper together with \cite{Z:2} and a different proof of universal noncollapsing due to Chen and Zhu \cite{ChZ:1} lead to a simplified proof of the Poincaré conjecture without using reduced distance and reduced volume. | |
| dc.description | more references added, especially [CL]; some details added on p12-14 | |
| dc.identifier | https://arxiv.org/abs/0812.2460 | |
| dc.identifier | http://arxiv.org/abs/0812.2460 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220757 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C44 | |
| dc.title | Heat kernel bounds, ancient $κ$ solutions and the Poincaré conjecture | |
| dc.type | text |