{"paper":{"title":"Maximising Neumann eigenvalues on rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Dorin Bucur, Katie Gittins, Michiel van den Berg","submitted_at":"2015-12-01T11:01:11Z","abstract_excerpt":"We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in $\\mathbb{R}^2$ with a measure or perimeter constraint. We show that the rectangle with measure $1$ which maximises the $k$'th Neumann eigenvalue converges to the unit square in the Hausdorff metric as $k\\rightarrow \\infty$. Furthermore, we determine the unique maximiser of the $k$'th Neumann eigenvalue on a rectangle with given perimeter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00224","kind":"arxiv","version":4},"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"}