{"paper":{"title":"A dimension-free interpolation of Caffarelli's contraction theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Bader Ammari","submitted_at":"2026-05-23T07:30:20Z","abstract_excerpt":"We prove global Lipschitz estimates for Brenier maps between probability measures on $\\mathbb{R}^n$ whose densities belong to the family $$\n  \\rho_{U,\\,p}=Z_{U,\\, p}^{-1}\\exp(-\\Theta_p(U)), \\qquad\n  \\Theta_p(t)=p\\log\\Bigl(1+\\frac{t}{p}\\Bigr),\n  \\qquad p\\in[n,+\\infty], $$ with finite normalization constant $Z_{U,\\, p}$, and with the convention $\\Theta_{\\infty}(t)=t$. We allow different parameters for source and target, $d,D\\in[n,+\\infty]$, with $d\\le D$. Our global estimate is uniform in $n,d,D$, and in the case $d=D<+\\infty$, it improves the bounds of arXiv:2404.05456 by removing their exponen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24443","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/2605.24443/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"}