{"paper":{"title":"The Steklov and Laplacian spectra of Riemannian manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Alexandre Girouard, Asma Hassannezhad, Bruno Colbois","submitted_at":"2018-10-01T14:08:44Z","abstract_excerpt":"Given two compact Riemannian manifolds with boundary $M_1$ and $M_2$ such that their respective boundaries $\\Sigma_1$ and $\\Sigma_2$ admit neighborhoods $\\Omega_1$ and $\\Omega_2$ which are isometric, we prove the existence of a constant $C$, which depends only on the geometry of $\\Omega_1\\cong\\Omega_2$, such that $|\\sigma_k(M_1)-\\sigma_k(M_2)|\\leq C$ for each $k\\in\\mathbb{N}$. This follows from a quantitative relationship between the Steklov eigenvalues $\\sigma_k$ of a compact Riemannian manifold $M$ and the eigenvalues $\\lambda_k$ of the Laplacian on its boundary. Our main result states that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00711","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"}