{
  "abstract": "In this paper we establish removable singularities results for Einstein metrics and for metrics with Ricci curvature bounded below. Let $n\\geq 2$. On a closed $n$-manifold, we show that an $L^\\infty$-Riemannian metric whose Ricci curvature is bounded below outside a singular set of codimension $> 3- \\frac{1}{n-1}$ canonically extends to an $\\mathrm{RCD}$ space. As a consequence, using a new removable singularity theorem for Einstein metrics, we prove that in dimension $4$ any Einstein metric with $L^\\infty$ singularities of codimension $>3-\\frac{1}{3}$ extends smoothly across the singular set, possibly after changing the smooth structure. In higher dimensions, we construct a $C^{1,α}$-Riemannian manifold structure on the regular set of a non-collapsed $\\mathrm{RCD}$ space that is a Riemannian manifold with bounded $|\\mathrm{Ric}|$ outside a set of codimension $>2$. Our results can be used to give a proof of Schoen's conjecture on scalar curvature singularities for metrics that are either continuous, or $L^\\infty$ and sufficiently close to a smooth background metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01464",
  "author_total": 2,
  "authors": [
    {
      "name": "Gioacchino Antonelli"
    },
    {
      "name": "Gábor Székelyhidi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frq9paxt4zpsp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01464",
  "fulltext_url": null,
  "id": "frq9paxt4zpsp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01464",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7206197294",
  "pdf_url": "https://arxiv.org/pdf/2609.01464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frq9paxt4zpsp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Removability of non-isolated singularities for Einstein metrics and RCD spaces",
  "title_text": "Removability of non-isolated singularities for Einstein metrics and RCD spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/frq9paxt4zpsp",
  "venue": "arXiv",
  "versions": []
}