{
  "abstract": "We prove that the optimal constant in the Chang--Marshall inequality is $e$, as conjectured by Andreev and Matheson. More precisely, if $f$ is analytic in the unit disk, vanishes to order $m\\geq1$ at the origin, and has normalized Dirichlet integral $d\\leq1$, then the boundary mean of $e^{|f|^2}$ is at most $e^{d/m}$. Equality holds precisely for monomials. The proof uses an auxiliary closed planar curve and the isoperimetric inequality to establish monotonicity of the exponential functional along normalized radial dilations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15378",
  "author_total": 2,
  "authors": [
    {
      "name": "Rupert L. Frank"
    },
    {
      "name": "Paata Ivanisvili"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89v0tg26s6yzg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15378",
  "fulltext_url": null,
  "id": "89v0tg26s6yzg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15378",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7221806536",
  "pdf_url": "https://arxiv.org/pdf/2610.15378",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89v0tg26s6yzg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.15378",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15378"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The sharp constant in the Chang--Marshall inequality",
  "title_text": "The sharp constant in the Chang--Marshall inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/89v0tg26s6yzg",
  "venue": "arXiv",
  "versions": []
}