{"paper":{"title":"An Isoperimetric Result on High-Dimensional Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CA","math.IT","math.MG"],"primary_cat":"math.PR","authors_text":"Ayfer Ozgur, Leighton Pate Barnes, Xiugang Wu","submitted_at":"2018-11-20T20:59:05Z","abstract_excerpt":"We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\\mathbb{S}^{m-1}$, and let $\\mathbf{y}\\in \\mathbb{S}^{m-1}$ be a randomly chosen point on the sphere. What is the measure of the intersection of the $t$-neighborhood of the point $\\mathbf{y}$ with the subset $A$? We show that with high probability this intersection is approximately as large as the intersection that would occur with high probability if $A$ were a spherical cap o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10533","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":""},"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"}