{"paper":{"title":"Uniform stability of the ball with respect to the first Dirichlet and Neumann $\\infty-$eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel M. Salort, Joao V. da Silva, Julio D. Rossi","submitted_at":"2017-05-08T18:48:56Z","abstract_excerpt":"In this note we analyze how perturbations of a ball $\\mathfrak{B}_r \\subset \\mathbb{R}^n$ behaves in terms of their first (non-trivial) Neumann and Dirichlet $\\infty-$eigenvalues when a volume constraint $\\\\mathscr{L}^n(\\Omega) = \\mathscr{L}^n(\\mathfrak{B}_r)$ is imposed. Our main result states that $\\Omega$ is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume $\\mathfrak{B}_r$. In fact, we show that, if $$\n  |\\lambda_{1,\\infty}^D(\\Omega) - \\lambda_{1,\\infty}^D(\\mathfrak{B}_r)| = \\delta_1 \\quad \\text{and} \\quad |\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03046","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"}