{"paper":{"title":"The prescribed Hermitian-Yang-Mills flow I","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shing-Tung Yau, Xaokui Yang, Zhiyao Xiong","submitted_at":"2026-06-19T03:21:33Z","abstract_excerpt":"In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow:\n  $$\\frac{\\partial h}{\\partial t}=-\\Lambda_{\\omega_g}\\left(\\sqrt R^h\\right)+P$$\n  where $P\\in\\Gamma(M,E^*\\otimes\\bar{E}^*)$ is a prescribed Hermitian tensor associated with a holomorphic vector bundle $E$ over a K\\\"ahler (or Hermitian) manifold $(M,\\omega_g)$. We establish the long-time convergence of the flow to a limiting metric $h_{\\infty}$ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation\n  $$\\Lambda_{\\omega_g}\\left(\\sqrt R^{h_\\infty}\\right)=P,\n  $$\n  for a general "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21062","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/2606.21062/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"}