{
  "abstract": "Let $(X,d,p)$ be an $n$-dimensional noncollapsed Ricci limit space, where $n\\ge4$. Under an integral volume-deficit bound, we prove that the metric singular set has Hausdorff codimension at least four and sigma-finite $(n-4)$-dimensional Hausdorff measure. This establishes a special case of the codimension-four regularity conjecture. Moreover, the nonmanifold locus is closed and has locally finite $(n-4)$-dimensional Hausdorff measure, and its intersection with each bounded ball satisfies a tubular-volume estimate of order $r^4$. In dimension four, the nonmanifold points form a locally finite set. A flat quotient example shows that the codimension bound is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33995",
  "author_total": 1,
  "authors": [
    {
      "name": "Lingling Kong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3aqmr9mwyahje.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33995",
  "fulltext_url": null,
  "id": "3aqmr9mwyahje",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33995",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214740805",
  "pdf_url": "https://arxiv.org/pdf/2609.33995",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3aqmr9mwyahje.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33995",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33995"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Codimension-four regularity of noncollapsed Ricci limit spaces under an integral volume-deficit bound",
  "title_text": "Codimension-four regularity of noncollapsed Ricci limit spaces under an integral volume-deficit bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3aqmr9mwyahje",
  "venue": "arXiv",
  "versions": []
}