{"paper":{"title":"A weighted isoperimetric inequality in a wedge","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":"2012-10-04T13:30:02Z","abstract_excerpt":"Let $c, k_1,..., k_N $ be non-negative numbers, and define a measure $\\mu $ in the wedge $W:= \\{x\\in \\mathbb{R} ^N :\\, x_i >0, i=1,...,N\\} $ by $d\\mu = e^{c|x|^2} x_1 ^{k_1}...x_N ^{k_N} \\, dx $. It is shown that among all measurable subsets of $W$ with fixed $\\mu$ -measure, the intersection of $W$ with a ball centered at the origin renders the weighted perimeter relative to $W$ a minimum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1432","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"}