{
  "abstract": "In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: $$\\frac{\\partial h}{\\partial t}=-Λ_{ω_g}\\left(\\sqrt{-1} R^h\\right)+P$$ where $P\\inΓ(M,E^*\\otimes\\bar{E}^*)$ is a prescribed Hermitian tensor associated with a holomorphic vector bundle $E$ over a Kähler (or Hermitian) manifold $(M,ω_g)$. 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 $$Λ_{ω_g}\\left(\\sqrt{-1} R^{h_\\infty}\\right)=P, $$ for a general class of prescribed Hermitian tensors $P$. The crucial uniform $C^0$-estimate of $\\{h(t)\\}$ along the flow is obtained via a parabolic comparison principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.21062",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiyao Xiong"
    },
    {
      "name": "Xaokui Yang"
    },
    {
      "name": "Shing-Tung Yau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0kk9501ahgz0q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.21062",
  "fulltext_url": null,
  "id": "0kk9501ahgz0q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.21062",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7165644124",
  "pdf_url": "https://arxiv.org/pdf/2606.21062",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0kk9501ahgz0q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.21062",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.21062"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The prescribed Hermitian-Yang-Mills flow I",
  "title_text": "The prescribed Hermitian-Yang-Mills flow I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/0kk9501ahgz0q",
  "venue": "arXiv",
  "versions": []
}