{
  "abstract": "In this paper, we study the Weyl problem for noncompact convex surfaces in hyperbolic $3$-space $\\mathbb{H}^3$. We prove that any planar CBB$(-1)$ surface with countably many ends can be isometrically embedded as the boundary of a closed convex subset $X\\subset\\mathbb{H}^3$ such that each connected component of the ideal boundary of $X$ is either a round disk or a single point. By known rigidity results, such an embedding is unique up to isometries of $\\mathbb{H}^3$. Moreover, we show that the assumption of countably many ends can be dropped if Koebe's circle domain conjecture holds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35744",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinrong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fkd6ppf9fbq3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35744",
  "fulltext_url": null,
  "id": "3fkd6ppf9fbq3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35744",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
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      "arxiv",
      "math.GT"
    ],
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      "arxiv",
      "math.MG"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7223850761",
  "pdf_url": "https://arxiv.org/pdf/2610.35744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fkd6ppf9fbq3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.35744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Weyl Problem for Planar CBB$(-1)$ Surfaces in Hyperbolic $3$-Space",
  "title_text": "The Weyl Problem for Planar CBB(−1) Surfaces in Hyperbolic $3$-Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/3fkd6ppf9fbq3",
  "venue": "arXiv",
  "versions": []
}