{"paper":{"title":"Some inequalities of isoperimetric type for the c-affine surface area","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Arnon Chor, Shiri Artstein-Avidan","submitted_at":"2025-05-25T14:44:39Z","abstract_excerpt":"We study the c-affine surface area $\\Omega^c$, recently introduced by Sch\\\"utt, Werner and Yalikun. We show that on the class of ball-bodies, $\\Omega^c$ is maximized by a ball of radius $\\frac{n}{n+1}$, and that a Santal\\'o-type inequality holds: $\\Omega^c(K) \\Omega^c(K^c) \\leq \\Omega^c(\\frac{1}{2} B_2^n)^2$. We also produce some more intricate inequalities involving the surface area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19172","kind":"arxiv","version":4},"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/2505.19172/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"}