{"paper":{"title":"Isoperimetric inequality under Measure-Contraction property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Fabio Cavalletti, Flavia Santarcangelo","submitted_at":"2018-10-26T12:35:15Z","abstract_excerpt":"We prove that if $(X,\\mathsf d,\\mathfrak m)$ is an essentially non-branching metric measure space with $\\mathfrak m(X)=1$, having Ricci curvature bounded from below by $K$ and dimension bounded from above by $N \\in (1,\\infty)$, understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality \\`a la L\\'evy-Gromov holds true. Measure theoretic rigidity is also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11289","kind":"arxiv","version":1},"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"}