{"paper":{"title":"The Cheeger constant of a Jordan domain without necks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gian Paolo Leonardi, Giorgio Saracco, Robin Neumayer","submitted_at":"2017-04-24T14:22:00Z","abstract_excerpt":"We show that the maximal Cheeger set of a Jordan domain $\\Omega$ without necks is the union of all balls of radius $r = h(\\Omega)^{-1}$ contained in $\\Omega$. Here, $h(\\Omega)$ denotes the Cheeger constant of $\\Omega$, that is, the infimum of the ratio of perimeter over area among subsets of $\\Omega$, and a Cheeger set is a set attaining the infimum. The radius $r$ is shown to be the unique number such that the area of the inner parallel set $\\Omega^r$ is equal to $\\pi r^2$. The proof of the main theorem requires the combination of several intermediate facts, some of which are of interest in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07253","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}