{"paper":{"title":"Isoperimetric and stable sets for log-concave perturbations of Gaussian measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"C\\'esar Rosales","submitted_at":"2014-03-18T15:46:32Z","abstract_excerpt":"Let $\\Omega$ be an open half-space or slab in $\\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\\exp(\\omega(p)-c|p|^2)$, where $c>0$ and $\\omega$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\\partial\\Omega$. In this work we follow a variational approach to show that half-spaces perpendicular to $\\partial\\Omega$ uniquely minimize the weighted perimeter in $\\Omega$ among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization of half-spaces parallel or p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4510","kind":"arxiv","version":3},"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"}