{
  "abstract": "Let $T_n$ be the infinite $n$-regular tree, $n\\ge3$. We prove that every finite connected vertex set $Ω\\subset T_n$ satisfies the sharp inequality \\[ σ_1(Ω)\\le \\frac{n}{(n-1)|Ω|+1}. \\] Equality holds if and only if $Ω$ is a ball. Since \\[ |δΩ|=(n-2)|Ω|+2, \\] the result is equivalently a sharp upper bound at fixed external boundary cardinality, and hence a discrete Weinstock inequality on $T_n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06067",
  "author_total": 2,
  "authors": [
    {
      "name": "Lili Wang"
    },
    {
      "name": "Tao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1xecaa07xhwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06067",
  "fulltext_url": null,
  "id": "f1xecaa07xhwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06067",
  "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.CO"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212077045",
  "pdf_url": "https://arxiv.org/pdf/2609.06067",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1xecaa07xhwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06067",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06067"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Weinstock Inequality on Regular Trees",
  "title_text": "Weinstock Inequality on Regular Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/f1xecaa07xhwf",
  "venue": "arXiv",
  "versions": []
}