{
  "abstract": "We study global smooth Calabi flows on polarized Kähler surfaces $(M,L)$, assuming uniformly bounded Sobolev constants and the algebraic conditions $χ(\\mathcal O_M)=1$ and $c_1(M)\\cdot c_1(L)>0$. Using the orbifold compactness theorem, we prove a uniform Bergman estimate, construct a normal test configuration for each geometric limit, and establish uniqueness of the extremal orbifold limit up to polarized holomorphic isometry. K-polystability then identifies the limit with the original surface and gives a constant scalar curvature Kähler metric. We also prove finite-group equivariant versions of these results. Independently of the flow, we obtain a uniform Bergman lower bound for polarized cscK surfaces with bounded volume and Sobolev constants and $|S|\\leq1$. We illustrate the hypotheses with nonstationary flows near a product cscK metric on $\\mathbb P^1\\times\\mathbb P^1$ and near Calabi's non-cscK extremal metric on the first Hirzebruch surface. Their controlled-cone energy inequalities follow from elementary calculations and continuity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01968",
  "author_total": 3,
  "authors": [
    {
      "name": "Haozhao Li"
    },
    {
      "name": "Bing Wang"
    },
    {
      "name": "Kai Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9q32afn080rnd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01968",
  "fulltext_url": null,
  "id": "9q32afn080rnd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01968",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9q32afn080rnd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Calabi flow on polarized Kähler surfaces",
  "title_text": "Calabi flow on polarized Kähler surfaces",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/9q32afn080rnd",
  "venue": "arXiv",
  "versions": []
}