{
  "abstract": "We prove that every Gromov elliptic domain $Ω$ in a complex manifold has the following property, which we call meromorphic pseudoconvexity: each boundary point has a neighborhood $V$ such that $Ω\\cap V$ becomes Stein after removing a set which is, locally in $Ω\\cap V$, the union of the polar sets of finitely many meromorphic functions on $Ω\\cap V$. Since meromorphic functions on Hartogs figures extend to their hulls, it follows that, for a domain $Ω=\\operatorname{int}\\overlineΩ$ in a Stein manifold, Gromov ellipticity is equivalent to being Oka and Stein, and also to being Oka and admitting a complete Kähler metric. This complements a theorem of Matsumura and the author that every weakly pseudoconvex Oka manifold admitting a positive line bundle is elliptic. As applications, we show that the Oka manifolds $\\mathbb C^n\\setminus\\overline{\\mathbb B^n}$ and $\\mathbb C^n\\setminus\\mathbb R^n$, $n\\geq2$, are not elliptic, and that no proper domain with Lipschitz boundary in $\\mathbb P^n$, $n\\geq2$, is elliptic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20574",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuta Kusakabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgrqb8423dszx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20574",
  "fulltext_url": null,
  "id": "fgrqb8423dszx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20574",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7222296253",
  "pdf_url": "https://arxiv.org/pdf/2610.20574",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgrqb8423dszx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20574",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20574"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Every Gromov elliptic domain is meromorphically pseudoconvex",
  "title_text": "Every Gromov elliptic domain is meromorphically pseudoconvex",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fgrqb8423dszx",
  "venue": "arXiv",
  "versions": []
}