{"paper":{"title":"Inequalities between Dirichlet and Neumann eigenvalues in large dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"N. Filonov","submitted_at":"2026-06-29T10:55:17Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $R^d$. Denote by $\\lambda_k$ (resp. $\\mu_k$) the eigenvalues of the Laplace operator in $\\Omega$ with Dirichlet (resp. Neumann) boundary conditions. Denote by $\\Psi = \\Psi (d,k,\\Omega)$ the shift of indices in the inequality $\\mu_{k+\\Psi} \\le \\lambda_k$. We are interested to describe the behaviour of $\\Psi$ for large $d$. We prove that a) $\\Psi (d,1,\\Omega) \\ge C (e/2)^d$ for all domains $\\Omega$; and b) $\\Psi (d,k,\\Omega) \\ge C (e/2)^d$ for all $k$ and all convex domains $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30120","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30120/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}