{
  "abstract": "Let $Ω\\subset\\mathbb{C}^n$ be a bounded hyperconvex domain admitting a negative plurisubharmonic exhaustion function $u$ such that $-u(z)\\le C\\exp[-η(\\log(1/δ_Ω(z)))]$ near the boundary, where $η$ is nondecreasing with $\\lim_{t\\rightarrow+\\infty}η(t)=+\\infty$. We present a lower bound for the Bergman distance $d_{B,Ω}(z_0,z)$ by counting the iterates of a function determined by the generalized inverse of $η$. The bound tends to infinity as $z\\rightarrow\\partialΩ$ for every such $η$; moreover, it recovers several known estimates. The proof combines a one-sided localization of Green sublevel sets with boundary estimates for the Bergman kernel and a capacity--volume inequality. We also obtain an upper bound for the Bergman distance along the axis of a family of complete Hartogs domains whose fiber radii decay faster than every positive power of the boundary distance in the base disc.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34339",
  "author_total": 2,
  "authors": [
    {
      "name": "Bo-Yong Chen"
    },
    {
      "name": "Yuanpu Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1eqnv70x47v03.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34339",
  "fulltext_url": null,
  "id": "1eqnv70x47v03",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34339",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7223889430",
  "pdf_url": "https://arxiv.org/pdf/2610.34339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1eqnv70x47v03.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative hyperconvexity and the Bergman distance",
  "title_text": "Quantitative hyperconvexity and the Bergman distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1eqnv70x47v03",
  "venue": "arXiv",
  "versions": []
}