{"paper":{"title":"A Morse index theorem for elliptic operators on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Christopher K.R.T. Jones, Graham Cox, Jeremy L. Marzuola","submitted_at":"2014-04-23T20:55:25Z","abstract_excerpt":"Given a selfadjoint, elliptic operator $L$, one would like to know how the spectrum changes as the spatial domain $\\Omega \\subset \\mathbb{R}^d$ is deformed. For a family of domains $\\{\\Omega_t\\}_{t\\in[a,b]}$ we prove that the Morse index of $L$ on $\\Omega_a$ differs from the Morse index of $L$ on $\\Omega_b$ by the Maslov index of a path of Lagrangian subspaces on the boundary of $\\Omega$. This is particularly useful when $\\Omega_a$ is a domain for which the Morse index is known, e.g. a region with very small volume. Then the Maslov index computes the difference of Morse indices for the \"origin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5981","kind":"arxiv","version":2},"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"}