{"paper":{"title":"Courant-sharp eigenvalues of Neumann 2-rep-tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"David Fajman, Michael Bersudsky, Ram Band","submitted_at":"2015-07-13T12:00:39Z","abstract_excerpt":"We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\\sqrt{2}$ (also known as the A4 paper). In $\\R^{n}$ the domains are boxes which generalize the mentioned planar rectangle. The symmetries of those domains reveal a special structure of their eigenfunctions, which we call folding\\textbackslash{}unfolding. This structure affects the nodal set of the eigenfunctions, which in turn allows to derive necessary conditions for Courant-sharpness. In addition, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03410","kind":"arxiv","version":3},"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"}