{"paper":{"title":"Self-Intersection of Optimal geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.MG","authors_text":"Fabio Cavalletti, Martin Huesmann","submitted_at":"2012-11-28T09:07:38Z","abstract_excerpt":"Let $(X,d,m)$ be a geodesic metric measure space. Consider a geodesic $\\mu_{t}$ in the $L^{2}$-Wasserstein space. Then as $s$ goes to $t$ the support of $\\mu_{s}$ and the support of $\\mu_{t}$ have to overlap, provided an upper bound on the densities holds. We give a more precise formulation of this self-intersection property. We consider for each $t$ the set of times for which a geodesic belongs to the support of $\\mu_{t}$ and we prove that $t$ is a point of Lebesgue density 1 for this set, in the integral sense. Our result applies to spaces satisfying $\\mathsf{CD}(K,\\infty)$. The non branchin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6547","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"}