{"paper":{"title":"Eigenvalue bounds of the Robin Laplacian with magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ayman Kachmar, Georges Habib","submitted_at":"2017-07-25T12:06:46Z","abstract_excerpt":"On a compact Riemannian manifold $M$ with boundary, we give an estimate for the eigenvalues $(\\lambda\\_k(\\tau,\\alpha))\\_k$ of the magnetic Laplacian with the Robin boundary conditions. Here, $\\tau$ is a positive number that defines the Robin condition and $\\alpha$ is a real differential 1-form on $M$ that represents the magnetic field. We express these estimates in terms of the mean curvature of the boundary, the parameter $\\tau$  and a lower bound of the Ricci curvature of $M$ (see Theorem \\ref{estimate1} and Corollary \\ref{corestimate}). The main technique is to use the Bochner formula estab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07939","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"}