{
  "abstract": "We prove Koebe's conjecture for John domains by showing that every planar John domain is conformally equivalent to a circle domain. Our proof is based on a geometric property of John domains, which we prove to be sufficient for uniformization by a circle domain. As a consequence, we obtain an alternative proof of Koebe's conjecture for inner uniform and Gromov hyperbolic domains, recovering results established in earlier work of the authors. Finally, we derive a necessary and sufficient condition for a domain to satisfy Koebe's conjecture by using Schramm's transboundary modulus and well-behaved exhaustions of circle domains constructed by the second author and Rajala.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31216",
  "author_total": 2,
  "authors": [
    {
      "name": "Christina Karafyllia"
    },
    {
      "name": "Dimitrios Ntalampekos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zmp8ebahfz3g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31216",
  "fulltext_url": null,
  "id": "4zmp8ebahfz3g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31216",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.31216",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zmp8ebahfz3g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31216",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31216"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Koebe uniformization, John domains, and transboundary modulus",
  "title_text": "Koebe uniformization, John domains, and transboundary modulus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/4zmp8ebahfz3g",
  "venue": "arXiv",
  "versions": []
}