{"paper":{"title":"Iterative construction of Hermitian-Einstein metrics on stable bundles","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiaxuan Fan, Shing-Tung Yau, Xiaokui Yang, Zhiyao Xiong","submitted_at":"2026-06-29T10:55:35Z","abstract_excerpt":"Let $E$ be a stable holomorphic vector bundle over a compact K\\\"ahler (or Gauduchon) manifold $(M,\\omega_g)$. We show that for any real number $\\mu>0$ and any initial Hermitian metric $h_0$ on $E$, there exists a unique iteration sequence $\\{h_m\\}$ satisfying\n  $$\n  \\Lambda_{\\omega_g}\\left(\\sqrt{-1}R^{h_{m+1}}\\right)\n  =(\\lambda_E-\\mu)h_{m+1}+\\mu h_m,\n  $$\n  and $\\{h_m\\}$ converges smoothly to a Hermitian-Einstein metric $h_\\infty$ on $E$ satisfying\n  $$\n  \\Lambda_{\\omega_g}\\left(\\sqrt{-1}R^{h_{\\infty}}\\right)\n  =\\lambda_Eh_\\infty,\n  $$\n  where $\\lambda_E\\in \\mathbb R$ is the stability constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30121","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/2606.30121/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"}