{
  "abstract": "We establish an interior $C^2$ estimate for locally bounded plurisubharmonic Bedford-Taylor solutions of the complex Monge--Ampère equation $\\det(u_{i\\bar j})=f$ under weak quadratic growth bounds on sufficiently large balls, where $f$ is positive and Dini-continuous. We assume a distributional lower bound for the Laplacian of $f^{1/n}$. The main ingredient is a pseudo-$C^2$ estimate using the Green-function averaging error, valid also when $f$ is nonnegative. As an application, we prove that every entire Bedford-Taylor solution of $\\det(u_{i\\bar j})=1$ with weak quadratic growth is a real quadratic polynomial, resolving a conjecture of Gábor Székelyhidi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28375",
  "author_total": 2,
  "authors": [
    {
      "name": "Jingchen Hu"
    },
    {
      "name": "Li Sheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e03dh5kzq7w8f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28375",
  "fulltext_url": null,
  "id": "e03dh5kzq7w8f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28375",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223130538",
  "pdf_url": "https://arxiv.org/pdf/2610.28375",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e03dh5kzq7w8f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28375",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28375"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior $C^2$ Estimates and a Liouville Theorem for the Complex Monge--Ampère Equation",
  "title_text": "Interior C^2 Estimates and a Liouville Theorem for the Complex Monge--Ampère Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/e03dh5kzq7w8f",
  "venue": "arXiv",
  "versions": []
}