{"paper":{"title":"Super-Ricci flows and improved gradient and transport estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eva Kopfer","submitted_at":"2017-04-13T15:40:03Z","abstract_excerpt":"We show that the heat flow on super-Ricci flows in the sense of Sturm satisfies transport estimates with respect to every $L^p$-Kantorovich distance, $p\\in[1,\\infty]$. As an application we construct Brownian motions on time-dependent metric measure spaces and present transport estimates for their trajectories.\n  The proof is inspired by the approach from Savar\\'e and Bakry respectively and takes advantage of the self-improvement of the gradient estimates. For this we prove a refined version of Bochner's inequality under strengthened assumptions on the metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04177","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"}