{
  "abstract": "In this paper, we establish geometric consequences of our Type I scalar curvature estimate for finite-time solutions of the Kähler-Ricci flow on compact Kähler manifolds. We prove a uniform global diameter bound and a Type I diameter bound for every fibre of finite time holomorphic contraction. These estimates yield Gromov-Hausdorff convergence to a unique compact metric space homeomorphic to the normal Kähler space determined by the limiting cohomology class. We also establish a local partial $C^0$ estimate for the normalized flow and show that the tangent shrinkers are normal complex analytic varieties with log terminal singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22941",
  "author_total": 2,
  "authors": [
    {
      "name": "Wangjian Jian"
    },
    {
      "name": "Jian Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57mrk3k56dswr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22941",
  "fulltext_url": null,
  "id": "57mrk3k56dswr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22941",
  "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": "W7222954380",
  "pdf_url": "https://arxiv.org/pdf/2610.22941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57mrk3k56dswr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.22941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Type I estimates for the Kähler-Ricci flow II",
  "title_text": "Type I estimates for the Kähler-Ricci flow II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/57mrk3k56dswr",
  "venue": "arXiv",
  "versions": []
}