{
  "abstract": "In this paper, we study the rigidity of noncompact convex sets in hyperbolic 3-space. We prove that any intrinsic isometry between the boundaries of two closed, noncompact convex subsets of hyperbolic 3-space of dimension at least two extends to a global isometry of the ambient space, provided that their ideal boundaries are circle-type closed sets with countably many connected components. Moreover, the same conclusion holds if the ideal boundaries consist of finitely many mutually disjoint disks together with a set of one-dimensional Hausdorff measure zero. This result generalizes a recent rigidity theorem of Luo, Luo, and Rao by allowing the ideal boundaries to contain disk components. As a direct consequence, we establish a uniqueness result concerning the Weyl problem for convex surfaces in hyperbolic 3-space, as proposed by Luo and Wu. In particular, our approach provides an alternative proof of the discrete Schwarz lemma. The proof uses Pogorelov's rigidity theorem for compact convex bodies in $\\mathbb{R}^3$, the Pogorelov map, and properties of locally convex surfaces in $\\mathbb{R}^3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15402",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinrong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ct52h5rhj2m46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15402",
  "fulltext_url": null,
  "id": "ct52h5rhj2m46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15402",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7164936609",
  "pdf_url": "https://arxiv.org/pdf/2606.15402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ct52h5rhj2m46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2606.15402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15402"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity Theorems for the Weyl Problem of Convex Surfaces in Hyperbolic 3-Space",
  "title_text": "Rigidity Theorems for the Weyl Problem of Convex Surfaces in Hyperbolic 3-Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/ct52h5rhj2m46",
  "venue": "arXiv",
  "versions": []
}