{"paper":{"title":"Measure contraction property, curvature exponent and geodesic dimension of sub-Finsler $\\ell^p$-Heisenberg groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Kenshiro Tashiro, Samu\\\"el Borza","submitted_at":"2023-05-26T08:21:04Z","abstract_excerpt":"We initiate the study of synthetic curvature-dimension bounds in sub-Finsler geometry. More specifically, we investigate the measure contraction property $\\mathsf{MCP}(K, N)$, and the geodesic dimension on the Heisenberg group equipped with an $\\ell^p$-sub-Finsler norm. We show that for $p\\in(2,\\infty]$, the $\\ell^p$-Heisenberg group fails to satisfy any of the measure contraction properties. On the other hand, if $p\\in(1,2)$, then it satisfies the measure contraction property $\\mathsf{MCP}(K, N)$ if and only if $K \\leq 0$ and $N \\geq N_p$, where the curvature exponent $N_p$ is strictly greate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16722","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/2305.16722/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"}