{"paper":{"title":"First eigenvalue estimates on complete K\\\"ahler manifolds","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mingwei Wang, Xiaokui Yang","submitted_at":"2025-07-12T08:49:29Z","abstract_excerpt":"Let $ (M,\\omega_g) $ be a complete K\\\"ahler manifold of complex dimension $n$. We prove that if the holomorphic sectional curvature satisfies $\\mathrm{HSC} \\geq 2 $, then the first eigenvalue $\\lambda_1$ of the Laplacian on $(M,\\omega_g)$ satisfies $$ \\lambda_1 \\geq \\frac{320(n-1)+576}{81(n-1)+144}.$$ This result is established through a new Bochner-Kodaira type identity specifically developed for holomorphic sectional curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09203","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/2507.09203/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"}