A uniform Sobolev inequality under Ricci flow
| dc.creator | Zhang, Qi S. | |
| dc.date | 2007-06-12 | |
| dc.date | 2007-08-29 | |
| dc.date.accessioned | 2026-07-07T08:26:01Z | |
| dc.date.available | 2026-07-07T08:26:01Z | |
| dc.description | Let ${\bf M}$ be a compact Riemannian manifold and the metrics $g=g(t)$ evolve by the Ricci flow. We prove the following result. The Sobolev imbedding by Aubin or Hebey, perturbed by a scalar curvature term and modulo sharpness of constants, holds uniformly for $({\bf M}, g(t))$ for all time if the Ricci flow exists for all time; and if the Ricci flow develops a singularity in finite time, then the same Sobolev imbedding holds uniformly after a standard normalization. As a consequence, long time non-collapsing results are derived, which improve Perelman's local non-collapsing results. An application to 3-d Ricci flow with surgery is also presented. | |
| dc.description | An application to 3-d Ricci flow with surgery is added | |
| dc.identifier | https://arxiv.org/abs/0706.1594 | |
| dc.identifier | http://arxiv.org/abs/0706.1594 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136807 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58J35 | |
| dc.title | A uniform Sobolev inequality under Ricci flow | |
| dc.type | text |