{
  "abstract": "We extend the quantitative Dirichlet theorem of Gui, Hu, and Li \\cite{GuiHuLi2026} to Robin torsional rigidity. For every fixed $β>0$, we prove that the regular $N$-gon uniquely maximizes Robin torsional rigidity among tangential $N$-gons of prescribed area. Our explicit perimeter deficit bound contains the Dirichlet deficit obtained by Gui, Hu, and Li \\cite{GuiHuLi2026} and an additional Robin term that is positive for nonregular tangential polygons. For triangles, we answer the fixed-area optimization problem recorded as open by Keady and Wiwatanapataphee \\cite[Appendix A.1.2]{KeadyWiwatanapataphee2016}. We also establish strict monotonicity along equal-area regular polygons as the number of sides increases, with an explicit bound for each consecutive gap. The proof combines mixed Robin--Neumann triangular cells, spectral estimates for angular concavity, and a quantitative scaling estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21417",
  "author_total": 4,
  "authors": [
    {
      "name": "Changfeng Gui"
    },
    {
      "name": "Yeyao Hu"
    },
    {
      "name": "Qinfeng Li"
    },
    {
      "name": "Hang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5msq9s3hvg2ww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21417",
  "fulltext_url": null,
  "id": "5msq9s3hvg2ww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21417",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7222465591",
  "pdf_url": "https://arxiv.org/pdf/2610.21417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5msq9s3hvg2ww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A quantitative Robin Pólya--Szegő theorem for tangential polygons",
  "title_text": "A quantitative Robin Pólya--Szegő theorem for tangential polygons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/5msq9s3hvg2ww",
  "venue": "arXiv",
  "versions": []
}