{
  "abstract": "We study the rate at which the $p$-Bergman metric approaches the Carathéodory metric on convex domains with measures comparable to $δ^αdV$, $α>-1$. On smooth convex domains of finite type the logarithmic coefficient is bounded above by the harmonic-measure average of the tangential multitype dimension plus $1+α$, with equality when almost every endpoint of the extremal disc is coercive. For a class of convex domains in $\\mathbb{C}^2$ with $C^4$ boundary and rank-one real tangential contact along an axis disc, a winding number distinguishes the coefficient $2+α$ from an upper bound $7/4+α$; quartic contact makes the latter bound exact. The exact value holds along the entire axis of explicit real-algebraic strongly pseudoconvex domains, including perturbations without the weighted circle action, although their pointwise boundary models agree up to unitary equivalence with those of a domain having coefficient $2+α$. A $C^2$ example has negative winding but coefficient $2+α$, with a $-\\frac12\\log\\log p$ correction, so boundary regularity is essential to the gap theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08616",
  "author_total": 1,
  "authors": [
    {
      "name": "Gunhee Cho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6j18261j8kza6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08616",
  "fulltext_url": null,
  "id": "6j18261j8kza6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08616",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6j18261j8kza6.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "How the $p$-Bergman metric approaches the Carathéodory metric",
  "title_text": "How the p-Bergman metric approaches the Carathéodory metric",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/6j18261j8kza6",
  "venue": "arXiv",
  "versions": []
}