{"paper":{"title":"A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincar\\'e inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.DG","authors_text":"Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo","submitted_at":"2010-07-09T14:30:43Z","abstract_excerpt":"Let $\\mathbb{M}$ 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:\n  1 The volume doubling property; 2 The Poincar\\'e inequality; 3 The parabolic Harnack inequality.\n  The key ingredient is the study of dimensional reverse log-Sobolev inequalities for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1600","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}