{
  "abstract": "In this paper, we study the torsion problem on bounded, smooth, strictly horo-convex domains in hyperbolic space. We prove that if the diameter of the domain is sufficiently small, then $-\\sqrt{u}$ is strictly convex, where $u$ denotes the torsion function. The main ingredients of our proof are the constant rank theorem, a boundary convexity estimate, and a deformation argument for the domain. We also show that the exponent $1/2$ is optimal, even among strictly horo-convex domains of arbitrarily small diameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02516",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei Zhang"
    },
    {
      "name": "Qi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41bd9am6fcj69.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02516",
  "fulltext_url": null,
  "id": "41bd9am6fcj69",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02516",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7207801628",
  "pdf_url": "https://arxiv.org/pdf/2609.02516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41bd9am6fcj69.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Power convexity of the torsion function on horo-convex domains in hyperbolic space",
  "title_text": "Power convexity of the torsion function on horo-convex domains in hyperbolic space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/41bd9am6fcj69",
  "venue": "arXiv",
  "versions": []
}