{"paper":{"title":"On the higher Cheeger problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Enea Parini, Vladimir Bobkov","submitted_at":"2017-06-21T09:23:41Z","abstract_excerpt":"We develop the notion of higher Cheeger constants for a measurable set $\\Omega \\subset \\mathbb{R}^N$. By the $k$-th Cheeger constant we mean the value \\[h_k(\\Omega) = \\inf \\max \\{h_1(E_1), \\dots, h_1(E_k)\\},\\] where the infimum is taken over all $k$-tuples of mutually disjoint subsets of $\\Omega$, and $h_1(E_i)$ is the classical Cheeger constant of $E_i$. We prove the existence of minimizers satisfying additional \"adjustment\" conditions and study their properties. A relation between $h_k(\\Omega)$ and spectral minimal $k$-partitions of $\\Omega$ associated with the first eigenvalues of the $p$-L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07282","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"}