{
  "abstract": "We study the polynomial convexity of smooth totally real discs contained in the boundaries of strongly pseudoconvex domains in $\\mathbb{C}^2$. Using Wermer's classical example, we construct a bounded domain with smooth strongly pseudoconvex boundary containing a non-polynomially convex totally real disc. We also construct a nonsingular Levi-flat hypersurface in a non-Runge domain containing such a disc. This provides a partial negative answer, to a conjecture proposed in an earlier work. Furthermore, we prove that the Wermer graph over the closed disc of radius $R$ is polynomially convex for every $R\\in (0,1)$. Finally, we establish a sufficient condition for the polynomial convexity of totally real discs contained in the smoothly bounded strongly pseudoconvex domains in $\\mathbb{C}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02004",
  "author_total": 1,
  "authors": [
    {
      "name": "Golam Mostafa Mondal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezsprdf20rkg3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02004",
  "fulltext_url": null,
  "id": "ezsprdf20rkg3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02004",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezsprdf20rkg3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Polynomial convexity and non-polynomial convexity of totally real discs in $\\mathbb{C}^2$",
  "title_text": "Polynomial convexity and non-polynomial convexity of totally real discs in ℂ^2",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ezsprdf20rkg3",
  "venue": "arXiv",
  "versions": []
}