{"paper":{"title":"Mean curvature bounds and eigenvalues of Robin Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.OC"],"primary_cat":"math.SP","authors_text":"Konstantin Pankrashkin, Nicolas Popoff","submitted_at":"2014-07-11T09:35:17Z","abstract_excerpt":"We consider the Laplacian with attractive Robin boundary conditions, \\[ Q^\\Omega_\\alpha u=-\\Delta u, \\quad \\dfrac{\\partial u}{\\partial n}=\\alpha u \\text{ on } \\partial\\Omega, \\] in a class of bounded smooth domains $\\Omega\\in\\mathbb{R}^\\nu$; here $n$ is the outward unit normal and $\\alpha>0$ is a constant. We show that for each $j\\in\\mathbb{N}$ and $\\alpha\\to+\\infty$, the $j$th eigenvalue $E_j(Q^\\Omega_\\alpha)$ has the asymptotics \\[ E_j(Q^\\Omega_\\alpha)=-\\alpha^2 -(\\nu-1)H_\\mathrm{max}(\\Omega)\\,\\alpha+{\\mathcal O}(\\alpha^{2/3}), \\] where $H_\\mathrm{max}(\\Omega)$ is the maximum mean curvature "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3087","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"}