Weak curvature conditions and functional inequalities
| dc.creator | Lott, John | |
| dc.creator | Villani, Cedric | |
| dc.date | 2005-06-23 | |
| dc.date | 2006-10-22 | |
| dc.date.accessioned | 2026-07-07T06:42:31Z | |
| dc.date.available | 2026-07-07T06:42:31Z | |
| dc.description | We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of transport of measures. We show that DM, along with a doubling condition on m, implies a scale-invariant local Poincare inequality. We show that if (X,d,m) has nonnegative N-Ricci curvature and has unique minimizing geodesics between almost all pairs of points then it satisfies DM, with constant 2^N. The condition DM is preserved by measured Gromov-Hausdorff limits. We then prove a Sobolev inequality for measured length spaces with N-Ricci curvature bounded below by K>0. Finally, we prove a sharp global inequality. | |
| dc.description | final version | |
| dc.identifier | https://arxiv.org/abs/math/0506481 | |
| dc.identifier | http://arxiv.org/abs/math/0506481 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102066 | |
| dc.subject | Differential Geometry | |
| dc.title | Weak curvature conditions and functional inequalities | |
| dc.type | text |