{"paper":{"title":"Boundary regularity of optimal transport maps on convex domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Freid Tong, Tristan C. Collins","submitted_at":"2025-07-07T18:29:24Z","abstract_excerpt":"We study the regularity of optimal transport maps between convex domains with quadratic cost. For nondegenerate $C^{\\alpha}$-densities, we prove $C^{1, 1-\\varepsilon}$-regularity of the potentials up to the boundary. If in addition the boundary is $C^{1, \\alpha}$, we improve this to $C^{2, \\alpha}$-regularity. We also investigate pointwise $C^{1, 1}$-regularity at boundary points. We obtain a complete characterization of pointwise $C^{1, 1}$-regularity for planar polytopes in terms of the geometry of tangent cones. Furthermore, we study the regularity of optimal transport maps with degenerate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05395","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05395/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}