{
  "abstract": "This paper investigates an isoperimetric-type problem posed by L. A. Santaló, concerning convex surfaces in hyperbolic 3-space that minimize total mean curvature among all convex surfaces with fixed surface area. This problem asks for a characterization of the minimizers and for the optimal form of a Minkowski-type inequality in hyperbolic 3-space. In this work, we propose a conjectural description of the minimizers under certain regularity assumptions. We also construct a new family of convex surfaces as as potential minimizer candidates and establish a property of the singular points of any minimizer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01771",
  "author_total": 1,
  "authors": [
    {
      "name": "Fang Hong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7te5x78hzdf1t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01771",
  "fulltext_url": null,
  "id": "7te5x78hzdf1t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01771",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7163217718",
  "pdf_url": "https://arxiv.org/pdf/2606.01771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7te5x78hzdf1t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2606.01771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Santaló's Problem",
  "title_text": "On Santaló's Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/7te5x78hzdf1t",
  "venue": "arXiv",
  "versions": []
}