{"paper":{"title":"Higher codimension relative isoperimetric inequality outside a convex set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brian Krummel","submitted_at":"2017-10-13T06:29:17Z","abstract_excerpt":"We consider an isoperimetric inequality for $(m+1)$-dimensional area minimizing submanifolds of arbitrary codimension which lie outside a convex set $\\mathcal{K} \\subset \\mathbb{R}^{n+1}$ and are bounded by a submanifold of $\\mathbb{R}^{n+1} \\setminus \\mathcal{K}$ and the convex set $\\mathcal{K}$. We show that the least value of the isoperimetric ratio is attained for an $(m+1)$-dimensional flat half-disk of $\\mathbb{R}^{n+1}_+$. This extends prior work of Choe, Ghomi, and Ritor\\'{e} in codimension one and proves a conjecture of Choe in the case of relative area minimizers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04821","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"}