{"paper":{"title":"Lipschitz maps with prescribed local Lipschitz constants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Aidan Backus, Ng Ze-An","submitted_at":"2024-03-12T14:48:45Z","abstract_excerpt":"Let $\\Gamma$ be a closed subset of a complete Riemannian manifold $M$ of dimension $\\geq 2$, let $f: M \\to N$ be a Lipschitz map to a complete Riemannian manifold $N$, and let $\\psi$ be a continuous function which dominates the local Lipschitz constant of $f$. We construct a Lipschitz map which agress with $f$ on $\\Gamma$ and whose local Lipschitz constant is $\\psi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07702","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/2403.07702/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"}