{"paper":{"title":"Cheeger Inequalities for the Persistent Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Magnus Bakke Botnan, Rui Dong","submitted_at":"2026-06-01T20:10:48Z","abstract_excerpt":"We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes $\\mathcal{K}\\hookrightarrow \\mathcal{L}$. We introduce a persistent up $p$-Laplacian $\\Delta_{q,p,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$ for $p\\geq 1$. For $p=2$, this recovers the usual persistent up Laplacian, while for $p=1$ it yields a nonzero persistent Cheeger constant $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$. We prove a Cheeger-type inequality relating $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$ to the smallest nonzero eigenvalue of $\\Delta_{q,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02846","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}