{"paper":{"title":"McKean Rigidity for Cocompact Negatively Curved Manifolds and the \\(p\\)-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bo Zhu, Kuntao Jin","submitted_at":"2026-08-02T02:51:36Z","abstract_excerpt":"Let \\((M^m,g)\\) be a closed Riemannian manifold with \\(\\sec_g\\leq-1\\). We prove that the bottom spectrum of its universal cover attains McKean's lower bound if and only if the universal cover is hyperbolic space of constant sectional curvature \\(-1\\). More generally, for every \\(1<p<\\infty\\), the variational \\(p\\)-fundamental tone satisfies \\[\n  \\lambda_{1,p}(\\wti M)\n  \\geq\\left(\\frac{m-1}{p}\\right)^p, \\] and equality for some \\(p\\in(1,\\infty)\\) holds if and only if \\(\\wti M\\cong\\bH^m(-1)\\). In that case, equality holds for every \\(p\\in(1,\\infty)\\). The proof converts the two McKean defects of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00944","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/2608.00944/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"}