{"paper":{"title":"Isoperimetric estimates for the first Neumann eigenvalue of Hermite differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Francesco Chiacchio, Giuseppina di Blasio","submitted_at":"2011-03-29T14:53:01Z","abstract_excerpt":"We provide isoperimetric Szeg\\\"{o}-Weinberger type inequalities for the first nontrivial Neumann eigenvalue $\\mu_{1}(\\Omega)$ in Gauss space, where $\\Omega$ is a possibly unbounded domain of $\\mathbb{R}^{N}$. Our main result consists in showing that among all sets of $\\mathbb{R}^{N}$ symmetric about the origin, having prescribed Gaussian measure, $\\mu_{1}(\\Omega)$ is maximum if and only if $\\Omega$ is the euclidean ball centered at the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1101","kind":"arxiv","version":5},"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"}