{"paper":{"title":"Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.MG","authors_text":"Andrea Mondino, Fabio Cavalletti","submitted_at":"2015-02-23T15:44:51Z","abstract_excerpt":"We prove that if $(X,\\mathsf{d},\\mathfrak{m})$ is a metric measure space with $\\mathfrak{m}(X)=1$ having (in a synthetic sense) Ricci curvature bounded from below by $K>0$ and dimension bounded above by $N\\in [1,\\infty)$, then the classic L\\'evy-Gromov isoperimetric inequality (together with the recent sharpening counterparts proved in the smooth setting by E. Milman for any $K\\in \\mathbb{R}$, $N\\geq 1$ and upper diameter bounds) hold, i.e. the isoperimetric profile function of $(X,\\mathsf{d},\\mathfrak{m})$ is bounded from below by the isoperimetric profile of the model space. Moreover, if equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06465","kind":"arxiv","version":2},"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"}