{
  "abstract": "We prove that if $M$ is a connected Stein manifold of complex dimension at least three with the density property, then $M\\setminus K$ is a connected Oka manifold for every nonempty compact $K\\Subset M$ with smooth boundary whose Levi form has at least two nonnegative eigenvalues at every boundary point for local defining functions negative on $\\operatorname{int}K$. For compact sets in $\\mathbb{C}^n$ with smooth boundary, this settles both implications between pseudoconvexity of $\\partial K$ and the Oka property of $\\mathbb{C}^n\\setminus K$: pseudoconvexity is sufficient but not necessary for $n\\geq3$, and necessary but not sufficient for $n=2$. In dimension two, we give an explicit compact set in $\\mathbb{C}^2$ with strongly pseudoconvex boundary and non-Oka complement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34426",
  "author_total": 1,
  "authors": [
    {
      "name": "Yun-Heng Du"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bdf29kwzabx32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34426",
  "fulltext_url": null,
  "id": "bdf29kwzabx32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34426",
  "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/2610.34426",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bdf29kwzabx32.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34426",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34426"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Levi-form criterion for Oka complements",
  "title_text": "A Levi-form criterion for Oka complements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bdf29kwzabx32",
  "venue": "arXiv",
  "versions": []
}