{
  "abstract": "We study length ratios of simple closed geodesics on finite-type hyperbolic surfaces of positive genus. We allow cusps and fix the geodesic boundary lengths. Let $d$ be the dimension of the corresponding Teichmüller space $\\mathcal{T}_{\\mathbf{L}}(S)$. We prove that for every positive vector $(r_0,\\ldots,r_d)$, the set of surfaces carrying $d+1$ distinct essential interior simple closed geodesics with lengths proportional to this vector is dense in $\\mathcal{T}_{\\mathbf{L}}(S)$. In particular, one-holed tori with three distinct simple closed geodesics of equal length are dense. The proof uses high powers of Dehn twists, asymptotics of length differentials, and the Brouwer fixed-point theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24700",
  "author_total": 2,
  "authors": [
    {
      "name": "Nhat Minh Doan"
    },
    {
      "name": "Hanh Vo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25s0qjr3fzg46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24700",
  "fulltext_url": null,
  "id": "25s0qjr3fzg46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24700",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223003436",
  "pdf_url": "https://arxiv.org/pdf/2610.24700",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25s0qjr3fzg46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24700",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24700"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Density of length ratios on Teichmüller space",
  "title_text": "Density of length ratios on Teichmüller space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/25s0qjr3fzg46",
  "venue": "arXiv",
  "versions": []
}