{
  "abstract": "Bonk and Kleiner proved that if $G$ is a Gromov hyperbolic group whose boundary $\\partial_{\\infty}G$ is homeomorphic to an Ahlfors $Q$-regular metric $2$-sphere $Z$, and the Ahlfors regular conformal dimension of $Z$ is attained and equal to $Q$, then $G$ acts discretely, cocompactly, and isometrically on $\\mathbb{H}^3$. In this article, we extend the Bonk-Kleiner theorem to the setting of relatively hyperbolic groups. More precisely, we prove that if $(G,\\mathcal{H})$ is a relatively hyperbolic group whose Bowditch boundary is homeomorphic to an Ahlfors $Q$-regular metric $2$-sphere $Z$, with the Ahlfors regular conformal dimension of $Z$ attained and equal to $Q$, then $G$ acts discretely and isometrically on $\\mathbb{H}^3$, and every subgroup in $\\mathcal{H}$ is virtually $\\mathbb Z^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28346",
  "author_total": 2,
  "authors": [
    {
      "name": "Abhijit Pal"
    },
    {
      "name": "Rana Sardar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dnazk00144z7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28346",
  "fulltext_url": null,
  "id": "2dnazk00144z7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28346",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204826139",
  "pdf_url": "https://arxiv.org/pdf/2608.28346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dnazk00144z7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On 2-Sphere Bowditch Boundaries Attaining Conformal Dimension",
  "title_text": "On 2-Sphere Bowditch Boundaries Attaining Conformal Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/2dnazk00144z7",
  "venue": "arXiv",
  "versions": []
}