{"paper":{"title":"Prescribed Chern scalar curvatures on complete Hermitian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The existence of metrics with prescribed Chern scalar curvature holds on complete noncompact Hermitian manifolds in all dimensions.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Weike Yu","submitted_at":"2025-06-17T14:57:36Z","abstract_excerpt":"In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results [J. Differential Geom., 21 (1985): 269-281] from Poincar\\'e disks to higher dimensional Hermitian manifolds."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results from Poincaré disks to higher dimensional Hermitian manifolds.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The prescribed curvature function and the Hermitian manifold satisfy decay or integrability conditions at infinity that permit the 2D existence argument to carry over to higher dimensions (implicit in the generalization statement).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generalizes Aviles-McOwen existence results for prescribed Chern scalar curvatures from Poincaré disks to higher-dimensional complete Hermitian manifolds.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The existence of metrics with prescribed Chern scalar curvature holds on complete noncompact Hermitian manifolds in all dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5a5434705fd2a485531fcdfada4b404853bf8534ee3f896f2368ea8bcd6fcda6"},"source":{"id":"2506.14592","kind":"arxiv","version":5},"verdict":{"id":"b1efe4df-f022-4fde-97e4-961df2e3bc88","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T09:11:33.910238Z","strongest_claim":"We investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results from Poincaré disks to higher dimensional Hermitian manifolds.","one_line_summary":"Generalizes Aviles-McOwen existence results for prescribed Chern scalar curvatures from Poincaré disks to higher-dimensional complete Hermitian manifolds.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The prescribed curvature function and the Hermitian manifold satisfy decay or integrability conditions at infinity that permit the 2D existence argument to carry over to higher dimensions (implicit in the generalization statement).","pith_extraction_headline":"The existence of metrics with prescribed Chern scalar curvature holds on complete noncompact Hermitian manifolds in all dimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.14592/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":1,"snapshot_sha256":"50badf5e81c5faf28c7cfaa5c27c97f29db3146cb0876fd9d38ee7ffa4e0a1d8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}