{
  "abstract": "Kerckhoff proved that the geodesic length function $\\ell_Ω$ of a filling $Ω$ on $S_g$ attains a unique minimum in Teichmüller space. Recent work of Ernesto Girondo et al. computed these minima for uniform fillings using the algebraic machinery of dessins d'enfants and Grothendieck-Belyi surfaces. We present an elementary optimization approach for $4$-regular topological uniform fillings, bypassing this framework. Furthermore, we analyze two special classes of non-uniform $4$-regular fillings using fat graphs and optimization techniques. We explicitly compute their minima and prove that in both classes, the minimum of these length functions is attained at a triangle surface.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10344",
  "author_total": 2,
  "authors": [
    {
      "name": "Subash Chandra Behera"
    },
    {
      "name": "Shiv Parsad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1k1ngxz1nz7p6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10344",
  "fulltext_url": null,
  "id": "1k1ngxz1nz7p6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10344",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7168267158",
  "pdf_url": "https://arxiv.org/pdf/2607.10344",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1k1ngxz1nz7p6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2607.10344",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10344"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minima of geodesic length functions for non-uniform filling systems",
  "title_text": "Minima of geodesic length functions for non-uniform filling systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1k1ngxz1nz7p6",
  "venue": "arXiv",
  "versions": []
}