{"paper":{"title":"Weighted isoperimetric inequalities in cones and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Mercaldo, Francesco Chiacchio, Friedemann Brock","submitted_at":"2011-07-27T08:09:21Z","abstract_excerpt":"This paper deals with weighted isoperimetric inequalities relative to cones of $\\mathbb{R}^{N}$. We study the structure of measures that admit as isoperimetric sets the intersection of a cone with balls centered at the vertex of the cone. For instance, in case that the cone is the half-space $\\mathbb{R}_{+}^{N}={x \\in \\mathbb{R}^{N} : x_{N}>0}$ and the measure is factorized, we prove that this phenomenon occurs if and only if the measure has the form $d\\mu=ax_{N}^{k}\\exp(c|x|^{2})dx $, for some $a>0$, $k,c\\geq 0$. Our results are then used to obtain isoperimetric estimates for Neumann eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5406","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":""},"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"}