{"paper":{"title":"Decomposition of geodesics in the Wasserstein space and the globalization property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Fabio Cavalletti","submitted_at":"2012-09-26T11:53:13Z","abstract_excerpt":"We will prove a decomposition for Wasserstein geodesics in the following sense: let $(X,d,m)$ be a non-branching metric measure space verifying $\\mathsf{CD}_{loc}(K,N)$ or equivalently $\\mathsf{CD}^{*}(K,N)$. We prove that every geodesic $\\mu_{t}$ in the $L^{2}$-Wasserstein space, with $\\mu_{t} \\ll m$, is decomposable as the product of two densities, one corresponding to a geodesic with support of codimension one verifying $\\mathsf{CD}^{*}(K,N-1)$, and the other associated with a precise one dimensional measure, provided the length map enjoys local Lipschitz regularity. The motivation for our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5909","kind":"arxiv","version":4},"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"}