A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
| hal.structure.identifier | Department of Mathematics | |
| dc.contributor.author | BAUDOIN, Fabrice | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONNEFONT, Michel | |
| dc.contributor.author | GAROFALO, Nicola | |
| dc.date.accessioned | 2024-04-04T02:22:50Z | |
| dc.date.available | 2024-04-04T02:22:50Z | |
| dc.date.created | 2011-03-03 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189680 | |
| dc.description.abstractEn | Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $\mu$. We show that if $L$ satisfies, with a non negative curvature parameter, the generalized curvature inequality introduced by the first and third named authors in \cite{BG}, then the following properties hold: 1 The volume doubling property; 2 The Poincaré inequality; 3 The parabolic Harnack inequality. The key ingredient is the study of dimensional reverse log-Sobolev inequalities for the heat semigroup and corresponding non-linear reverse Harnack type inequalities. Our results apply in particular to all Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and to wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00208-013-0961-y | |
| dc.subject.hal | Mathématiques [math]/Géométrie différentielle [math.DG] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1007.1600 | |
| bordeaux.journal | Mathematische Annalen | |
| bordeaux.page | 833-860 | |
| bordeaux.volume | 358 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3-4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00779388 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00779388v1 | |
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