{"paper":{"title":"On infinity thick quasiconvexity and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Miguel Garc\\'ia-Bravo, Toni Ikonen, Zheng Zhu","submitted_at":"2025-09-01T07:24:40Z","abstract_excerpt":"We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1,\\infty}(Z)$ has a Lipschitz representative. We prove that when the metric space is locally complete and the reference measure is infinitesimally doubling, the above property is equivalent to the space being very $\\infty$-thick quasiconvex up to a scale. That is, up to some scale, every pair of points can be joined by a family of quasiconvex curves that is not negligible for the $\\infty$-modulus.\n  As a first application, we prove a local-to-global improvement for the weak $(1,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01194","kind":"arxiv","version":2},"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/2509.01194/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"}