{
  "abstract": "We prove the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons: for every \\(n\\geq5\\), the regular $n$-gon is a strict local maximizer of torsional rigidity among convex $n$-gons of prescribed area. Our proof is entirely analytic. It builds on a locally stable proportional triangular covering inspired by Solynin and Zalgaller and an associated weighted Voronoi-type partition, together with a quantitative asymptotic analysis of the loss produced by truncating the overlapping triangles to the partition cells. The result is then obtained by establishing two key ingredients: the optimality of isosceles triangles for mixed torsional rigidity at fixed area and vertex angle, and a strict concavity property of the mixed torsional rigidity of isosceles triangles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23051",
  "author_total": 3,
  "authors": [
    {
      "name": "Beniamin Bogosel"
    },
    {
      "name": "Dorin Bucur"
    },
    {
      "name": "Ilaria Fragalà"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q623kyj54qa8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23051",
  "fulltext_url": null,
  "id": "3q623kyj54qa8",
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  "landing_url": "https://arxiv.org/abs/2609.23051",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.SP"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7214057587",
  "pdf_url": "https://arxiv.org/pdf/2609.23051",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q623kyj54qa8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23051",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23051"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons",
  "title_text": "Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3q623kyj54qa8",
  "venue": "arXiv",
  "versions": []
}