{"paper":{"title":"Optimal transportation between hypersurfaces bounding some strictly convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Emmanuel Humbert, Luc Molinet","submitted_at":"2015-07-09T12:54:50Z","abstract_excerpt":"Let $M,N$ be two smooth compact hypersurfaces of $\\mathbb{R}^n$ which bound strictly convex domains equipped with two absolutely continuous measures $\\mu$ and $\\nu$ (with respect to the volume measures of $M$ and $N$). We consider the optimal transportation from $\\mu$ to $\\nu$ for the quadratic cost. Let $(\\phi:m \\to \\mathbb{R},\\psi:N \\to \\mathbb{R})$ be some functions which achieve the supremum in the Kantorovich formulation of the problem and which satisfy\n  $$ \\psi (y) = \\inf_{z\\in M} \\Bigl( \\frac{1}{2}|y-z|^2 -\\varphi(z)\\Bigr);\n  \\varphi (x)=\\inf_{z\\in N} \\Bigl( \\frac{1}{2}|x-z|^2 -\\psi(z)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02489","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"}