{"paper":{"title":"Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.PR"],"primary_cat":"math.MG","authors_text":"Karl-Theodor Sturm","submitted_at":"2014-05-02T17:55:02Z","abstract_excerpt":"The goal of this paper is twofold: we study metric measure spaces $(X,d,m)$ with variable lower bounds for the Ricci curvature and we study pathwise coupling of Brownian motions. Given any lower semicontinuous function $k:X\\to \\mathbb R$ we introduce the curvature-dimension condition $CD(k,\\infty)$ which canonically extends the curvature-dimension condition $CD(K,\\infty)$ of Lott-Sturm-Villani for constant $K\\in \\mathbb R$. For infinitesimally Hilbertian spaces we prove i) its equivalence to an evolution-variation inequality $EVI_k$ which in turn extends the $EVI_K$-inequality of Ambrosio-Gigl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0459","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"}