{"paper":{"title":"Magnetic spectral bounds on starlike plane domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B. A. Siudeja, R. S. Laugesen","submitted_at":"2014-01-04T23:14:07Z","abstract_excerpt":"We develop sharp upper bounds for energy levels of the magnetic Laplacian on starlike plane domains, under either Dirichlet or Neumann boundary conditions and assuming a constant magnetic field in the transverse direction. Our main result says that $\\sum_{j=1}^n \\Phi \\big( \\lambda_j A/G \\big)$ is maximal for a disk whenever $\\Phi$ is concave increasing, $n \\geq 1$, the domain has area $A$, and $\\lambda_j$ is the $j$-th Dirichlet eigenvalue of the magnetic Laplacian $\\big( i\\nabla+ \\frac{\\beta}{2A}(-x_2,x_1) \\big)^2$. Here the flux $\\beta$ is constant, and the scale invariant factor $G$ penaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0850","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"}