{"paper":{"title":"On a magnetic characterization of spectral minimal partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Bernard Helffer, Thomas Hoffmann-Ostenhof","submitted_at":"2015-09-17T15:52:37Z","abstract_excerpt":"Given a bounded open set $\\Omega$ in $ \\mathbb R^n$ (or in a Riemannian manifold) and a partition of $\\Omega$ by $k$ open sets $D_j$, we consider the quantity $\\max_j \\lambda(D_j)$ where $\\lambda(D_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $D_j$. If we denote by $ \\mathfrak L_k(\\Omega)$ the infimum over all the $k$-partitions of $ \\max_j \\lambda(D_j)$, a minimal $k$-partition is then a partition which realizes the infimum. When $k=2$, we find the two nodal domains of a second eigenfunction, but the analysis of higher $k$'s is non trivial and quite interest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05304","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"}