{"paper":{"title":"Functional Inequalities on Weighted Riemannian Manifolds Subject to Curvature-Dimension Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eran Calderon","submitted_at":"2019-05-21T20:51:03Z","abstract_excerpt":"We establish new sharp inequalities of Poincar\\'{e} or log-Sobolev type, on geodesically-convex weighted Riemannian manifolds $(M,\\mathfrak{g},\\mu)$ whose (generalized) Ricci curvature $Ric_{\\mathfrak{g},\\mu,N}$ with effective dimension parameter $N\\in (-\\infty,\\infty]$ is bounded from below by a constant $K\\in\\mathbb{R}$, and whose diameter is bounded above by $D\\in (0,\\infty]$ (Curvature-Dimension-Diameter conditions $CDD(K,N,D)$). To this end we establish a general method which complements the `localization' theorem which has recently been established by B. Klartag. Klartag's Theorem is bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08866","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"}