{"paper":{"title":"Deep estimates for higher eigenvalues of the poly-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Zhengchao Ji","submitted_at":"2025-08-06T04:03:51Z","abstract_excerpt":"We investigate the lower bound for higher eigenvalues $\\lambda_i$ of the poly-Laplace operator on a bounded domain and improve the famous Li-Yau inequality and its related results. Firstly, we consider the low dimensional cases for the P\\'{o}lya conjecture, the clamped plate problem and the eigenvalue problem of the poly-Laplacian and deliver a series of deep eigenvalue inequalities for these problems respectively. Secondly, we establish a sharp lower bound for the eigenvalues of the poly-Laplacia in arbitrary dimension under some certain restrictive conditions. Finally, we provide an improved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04069","kind":"arxiv","version":2},"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/2508.04069/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"}