{
  "abstract": "Let $(X,d,p)$ be a noncollapsed pointed Gromov--Hausdorff limit of complete $n$-dimensional Riemannian manifolds with a uniform lower Ricci curvature bound, where $n\\ge4$. We assume that, on each bounded ball, the integral of the $3/2$ power of the small-ball volume deficit relative to the hyperbolic comparison volume is $O(r^3)$ as $r\\rightarrow0$. We prove that the metric singular set has Hausdorff dimension at most $n-3$ and sigma-finite $(n-3)$-dimensional Hausdorff measure, thus confirming a particular case of codimension-three regularity conjecture \\cite[Conjecture 2.4]{Naber2020}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21452",
  "author_total": 1,
  "authors": [
    {
      "name": "Lingling Kong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78cyn9p3bb6rw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21452",
  "fulltext_url": null,
  "id": "78cyn9p3bb6rw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21452",
  "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": "W7213905530",
  "pdf_url": "https://arxiv.org/pdf/2609.21452",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78cyn9p3bb6rw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21452",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21452"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Codimension-three regularity of noncollapsed Ricci limit spaces under an integral volume-deficit bound",
  "title_text": "Codimension-three regularity of noncollapsed Ricci limit spaces under an integral volume-deficit bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/78cyn9p3bb6rw",
  "venue": "arXiv",
  "versions": []
}