{"paper":{"title":"Non-isometric domains with the same Marvizi-Melrose invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lev Buhovsky, Vadim Kaloshin","submitted_at":"2018-01-03T11:02:29Z","abstract_excerpt":"For any strictly convex planar domain $\\Omega \\subset \\mathbb{R}^2$ with a $C^\\infty$ boundary one can associate an infinite sequence of spectral invariants introduced by Marvizi-Merlose. These invariants can generically be determined using the spectrum of the Dirichlet problem of the Laplace operator. A natural question asks if this collection is sufficient to determine $\\Omega$ up to isometry. In this paper we give a counterexample, namely, we present two non-isometric domains $\\Omega$ and $\\bar \\Omega$ with the same collection of Marvizi-Melrose invariants. Moreover, each domain has countab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00952","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"}