{"paper":{"title":"Complemented Brunn-Minkowski Inequalities and Isoperimetry for Homogeneous and Non-Homogeneous Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Emanuel Milman, Liran Rotem","submitted_at":"2013-08-26T20:33:32Z","abstract_excerpt":"Elementary proofs of sharp isoperimetric inequalities on a normed space $(\\mathbb{R}^n,||\\cdot||)$ equipped with a measure $\\mu = w(x) dx$ so that $w^p$ is homogeneous are provided, along with a characterization of the corresponding equality cases. When $p \\in (0,\\infty]$ and in addition $w^p$ is assumed concave, the result is an immediate corollary of the Borell-Brascamp-Lieb extension of the classical Brunn-Minkowski inequality, providing an elementary proof of a recent result of Cabr\\'e-Ros Oton-Serra. When $p \\in (-1/n,0)$, the relevant property turns out to be a novel \"complemented Brunn-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5695","kind":"arxiv","version":2},"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"}