{"paper":{"title":"Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Savo","submitted_at":"2019-04-16T08:09:50Z","abstract_excerpt":"We consider the first eigenvalue $\\lambda_1(\\Omega,\\sigma)$ of the Laplacian with Robin boundary conditions on a compact Riemannian manifold $\\Omega$ with smooth boundary, $\\sigma\\in\\bf R$ being the Robin boundary parameter. When $\\sigma>0$ we give a positive, sharp lower bound of $\\lambda_1(\\Omega,\\sigma)$ in terms of an associated one-dimensional problem depending on the geometry through a lower bound of the Ricci curvature of $\\Omega$, a lower bound of the mean curvature of $\\partial\\Omega$ and the inradius. When the boundary parameter is negative, the lower bound becomes an upper bound. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07525","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"}