{"paper":{"title":"Reverse isoperimetric problems under curvature constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Kateryna Tatarko, Kostiantyn Drach","submitted_at":"2023-03-04T02:18:07Z","abstract_excerpt":"In this paper we solve several reverse isoperimetric problems in the class of $\\lambda$-convex bodies, i.e., convex bodies whose curvature at each point of their boundary is bounded below by some $\\lambda > 0$.\n  We give an affirmative answer in $\\mathbb{R}^3$ to a conjecture due to Borisenko which states that the $\\lambda$-convex lens, i.e., the intersection of two balls of radius $1/\\lambda$, is the unique minimizer of volume among all $\\lambda$-convex bodies of given surface area.\n  Also, we prove a reverse inradius inequality: in model spaces of constant curvature and arbitrary dimension, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.02294","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/2303.02294/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"}