{
  "abstract": "In this paper, we study heat kernel estimates along the Kähler-Ricci flow with finite time noncollapsing singularities over a compact Kähler manifold. The starting point is the type-II scalar-curvature estimate, which gives the natural parabolic scale $r\\lesssim T-t$ near the singular time. By combining the distance distortion and space-time cut-off estimates of Bamler--Zhang with entropy, mean-value inequality, and conjugate heat-kernel estimates, we obtain two-sided Gaussian bounds and gradient bounds that are uniform on this scale. Under the global type-I scalar-curvature estimate, the same estimates hold on every scale. We then use these estimates and the monotonicity of the $W_1$-distance between conjugate heat flows to construct a canonical singular-time pseudo-distance. The distances $d_t$ (induced by $ω(t)$) converge uniformly to this pseudo-distance. Its metric quotient is the unique Gromov--Hausdorff limit. Finally, we apply Bamler's theory and the recent work of Hallgren--Zhang to obtain the following. Every fixed-base-point type-I blow-up admits a subsequential metric-flow limit whose time slices are singular shrinking Kähler--Ricci soliton spaces with normal complex-analytic and log-terminal structure, unique tangent cones, and a polarized Fano fibration. For moving base points, the limiting metric flow, equipped with its limiting conjugate heat flow, is a metric soliton precisely under an entropy-pinching condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21824",
  "author_total": 2,
  "authors": [
    {
      "name": "Lei Zhang"
    },
    {
      "name": "Zhenlei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agbpa4q9taqwp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21824",
  "fulltext_url": null,
  "id": "agbpa4q9taqwp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21824",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7222534429",
  "pdf_url": "https://arxiv.org/pdf/2610.21824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agbpa4q9taqwp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Finite Time Noncollapsing Kähler-Ricci Flow: Gaussian Type Heat Kernel, Gromov-Hausdorff Limits",
  "title_text": "Finite Time Noncollapsing Kähler-Ricci Flow: Gaussian Type Heat Kernel, Gromov-Hausdorff Limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/agbpa4q9taqwp",
  "venue": "arXiv",
  "versions": []
}