{"paper":{"title":"Super-Ricci Flows for Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.DG","authors_text":"Karl-Theodor Sturm","submitted_at":"2016-03-07T18:34:07Z","abstract_excerpt":"We introduce the notions of `super-Ricci flows' and `Ricci flows' for time-dependent families of metric measure spaces $(X,d_t,m_t)_{t\\in I}$. The former property is proven to be stable under suitable space-time versions of mGH-convergence. Uniformly bounded families of super-Ricci flows are compact. In the spirit of the synthetic lower Ricci bounds of Lott-Sturm-Villani for static metric measure spaces, the defining property for super-Ricci flows is the `dynamic convexity' of the Boltzmann entropy ${\\mathrm Ent}(.|m_t)$ regarded as a functions on the time-dependent geodesic space $({\\mathcal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02193","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"}