{
  "abstract": "For parabolic Ahlfors regular sets, we show that the bilateral weak geometric lemma (BWGL), bilateral approximation by unions of planes (BAUP), and corona decompositions by $Lip$(1,1/2) graphs (whose defining functions need not have half-order time derivatives in BMO) are equivalent. These geometric conditions do not imply the strong geometric lemma. A key tool is a parabolic version of Reifenberg's theorem for sets with holes, which we prove here. As an application of these geometric results, we prove that a parabolic Ahlfors $(n+2)$-regular measure $μ$ on $\\mathbb{R}^{d+1}$, $1\\leq n\\leq d-1$, is parabolic uniformly rectifiable if its support satisfies any of these equivalent conditions and the parabolic Riesz transform is bounded on $L^2(μ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42142",
  "author_total": 3,
  "authors": [
    {
      "name": "John Hoffman"
    },
    {
      "name": "Matthew Hyde"
    },
    {
      "name": "Mihalis Mourgoglou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s9xjm1rtma4n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42142",
  "fulltext_url": null,
  "id": "5s9xjm1rtma4n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42142",
  "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.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42142",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5s9xjm1rtma4n.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42142",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42142"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Parabolic Reifenberg Parametrizations and Corona Decompositions, with Applications to Singular Integrals",
  "title_text": "Parabolic Reifenberg Parametrizations and Corona Decompositions, with Applications to Singular Integrals",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/5s9xjm1rtma4n",
  "venue": "arXiv",
  "versions": []
}