{
  "abstract": "Let $X$ be a compact Kähler manifold with semi-ample canonical bundle. For any Kähler class $[ω]$, Jian--Shi--Song proved that there exists a unique cscK metric in the class $2πc_1(K_X)+\\varepsilon[ω]$ when $\\varepsilon \\in (0,\\varepsilon_0]$, using the properness criterion of Chen--Cheng. We prove that the cscK metrics in $2πc_1(K_X)+\\varepsilon[ω]$ converge, as $\\varepsilon\\downarrow0$, in the Gromov--Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model of $X$ as conjectured by Jian--Shi--Song. Based on the technique developed in this paper, we can also give a new proof the theorem of Lee--Tosatti--Zhang on the Gromov-Hausdorff convergence of the normalized Kähler--Ricci flow on $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21934",
  "author_total": 2,
  "authors": [
    {
      "name": "Frederick Tsz-Ho Fong"
    },
    {
      "name": "Junbang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c4x59y5kchwa9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21934",
  "fulltext_url": null,
  "id": "c4x59y5kchwa9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21934",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7222451010",
  "pdf_url": "https://arxiv.org/pdf/2610.21934",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c4x59y5kchwa9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21934",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21934"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Gromov-Hausdorff Convergence of Constant Scalar Curvature Kähler Metrics near the Canonical Class",
  "title_text": "Gromov-Hausdorff Convergence of Constant Scalar Curvature Kähler Metrics near the Canonical Class",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/c4x59y5kchwa9",
  "venue": "arXiv",
  "versions": []
}