{"paper":{"title":"An optimal Poincar\\'e-Wirtinger inequality in Gauss space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antoine Henrot, Barbara Brandolini, Cristina Trombetti, Francesco Chiacchio","submitted_at":"2012-09-28T10:06:47Z","abstract_excerpt":"Let $\\Omega$ be a smooth, convex, unbounded domain of $\\R^N$. Denote by $\\mu_1(\\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\\Omega$; we prove that $\\mu_1(\\Omega) \\ge 1$. The result is sharp since equality sign is achieved when $\\Omega$ is a $N$-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincar\\'e-Wirtinger inequality for functions belonging to the weighted Sobolev space $H^1(\\Omega,d\\gamma_N)$, where $\\gamma_N$ is the $N$-dimensional Gaussian measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6469","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"}