{"paper":{"title":"Curvature, Dolbeault-Dirac operators, and an $\\mathrm{L}^p$ index theorem on compact K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"C\\'edric Arhancet","submitted_at":"2024-01-08T19:30:32Z","abstract_excerpt":"We establish an $\\mathrm{L}^p$-index theorem for Dolbeault--Dirac operators on compact K\\\"ahler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$. For every $p \\in (1,\\infty)$, we prove that the closed $\\mathrm{L}^p$-realization $\\mathcal{D}_{E,p}$ of the Dolbeault-Dirac operator is bisectorial and admits a bounded $\\mathrm{H}^\\infty$ functional calculus on $\\mathrm{L}^p(\\Omega^{0,\\bullet}(M,E))$. We also show an $\\mathrm{L}^p$-Gaffney-type estimate, obtain $\\mathrm{L}^p$-Hodge decompositions, and prove that $\\mathcal{D}_{E,p}$ gives rise to an even compact Banach spectr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04203","kind":"arxiv","version":5},"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/2401.04203/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"}