{
  "abstract": "We study the explicit bounded pseudoconvex domain \\[ Ω=\\{(z_1,z_2,w)\\in\\mathbb C^3: |w|^2+|z_1z_2(z_1-z_2)|^2+|z_1|^8+|z_2|^8<1\\}. \\] Its boundary is real analytic and has finite D'Angelo type everywhere. We prove two assertions about the invariant metrics of this domain. First, $(Ω,k_Ω)$ is not Gromov hyperbolic; in fact arbitrarily fat Kobayashi geodesic triangles occur in every neighborhood of the type-$8$ point $(0,0,1)$. Second, the Carathéodory--Reiffen and Kobayashi--Royden metrics are not uniformly comparable. Along an explicit family of tangential directions the Carathéodory metric tends to zero while the Kobayashi metric has a positive limit. For the corresponding distances there are points $x_j,y_j\\to(0,0,1)$ such that $c_Ω(x_j,y_j)\\to0$ while $k_Ω(x_j,y_j)\\to\\infty$. This gives, among bounded real-analytic pseudoconvex domains, an affirmative answer to Problem~7.3.2 of the Several Complex Variables Problem List.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36124",
  "author_total": 1,
  "authors": [
    {
      "name": "Armen Edigarian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhjmfrbnsp12b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36124",
  "fulltext_url": null,
  "id": "fhjmfrbnsp12b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36124",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7224128849",
  "pdf_url": "https://arxiv.org/pdf/2610.36124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhjmfrbnsp12b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-comparable invariant metrics and failure of Gromov hyperbolicity on a real-analytic pseudoconvex domain",
  "title_text": "Non-comparable invariant metrics and failure of Gromov hyperbolicity on a real-analytic pseudoconvex domain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fhjmfrbnsp12b",
  "venue": "arXiv",
  "versions": []
}