{
  "abstract": "We give a parabolic proof of the Fu-Wang-Wu theorem for semilinear elliptic equations associated with generalized Gauduchon metrics. Fixing a Hermitian metric $ω$, we introduce a flow $\\partial_t v-Δv=ψ(\\vert\\nabla v\\vert^2)+\\langle B,dv\\rangle-c(t)-f(x)$ for the conformal factor, whose stationary points solve the semilinear elliptic equation of Fu-Wang-Wu. Under the growth condition $\\liminf_{t\\to+\\infty}ψ(t)/t^μ>0$ for some $μ>\\tfrac{1}{2}$, we prove that the flow exists uniquely for all time and converges; the limit solves the elliptic equation and is unique up to addition of a constant. Our convergence argument does not rely on a gradient-flow structure or a monotone energy functional. In particular, this recovers, by a flow method rather than the continuity method, the existence and uniqueness theorem of Fu-Wang-Wu on $k$-th generalized Gauduchon metrics, providing a new parabolic approach to their elliptic theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19887",
  "author_total": 1,
  "authors": [
    {
      "name": "Han Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d892zz02gkjmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19887",
  "fulltext_url": null,
  "id": "d892zz02gkjmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19887",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221904654",
  "pdf_url": "https://arxiv.org/pdf/2610.19887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d892zz02gkjmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A parabolic flow approach to generalized Gauduchon metrics",
  "title_text": "A parabolic flow approach to generalized Gauduchon metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/d892zz02gkjmj",
  "venue": "arXiv",
  "versions": []
}