{"paper":{"title":"Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Fabrice Baudoin, Nicola Garofalo","submitted_at":"2011-01-19T00:24:49Z","abstract_excerpt":"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 $\\mu$. Associated with $L$ one has \\textit{le carr\\'e du champ} $\\Gamma$ and a canonical distance $d$, with respect to which we suppose that $(M,d)$ be complete. We assume that $\\M$ is also equipped with another first-order differential bilinear form $\\Gamma^Z$ and we assume that $\\Gamma$ and $\\Gamma^Z$ satisfy the Hypothesis below. With these forms we introduce in \\eqref{cdi} below a generalization of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3590","kind":"arxiv","version":5},"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"}