{
  "abstract": "We study entire continuous plurisubharmonic solutions of the complex Monge-Ampère equation $(i\\partial\\bar\\partial u)^n=2^n n!μ$ in $\\mathbb{C}^n$, in the Bedford-Taylor sense, where $μ\\not\\equiv 0$ is a nonnegative locally finite Borel measure periodic with respect to a lattice of full real rank. We assume that $μ$ is locally dominated by complex Monge-Ampère measures of Hölder continuous plurisubharmonic functions, a condition under which the existence theorem of Demailly et al. yields Hölder continuous periodic correctors. Under this assumption, we prove that every such solution with positive two-sided quadratic growth can be written uniquely, up to an additive constant, as the sum of a real quadratic polynomial and a Hölder continuous periodic function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40004",
  "author_total": 2,
  "authors": [
    {
      "name": "Jingchen Hu"
    },
    {
      "name": "Xushan Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cr3rzhy3bvet.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40004",
  "fulltext_url": null,
  "id": "9cr3rzhy3bvet",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40004",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cr3rzhy3bvet.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Liouville theorem for plurisubharmonic functions with periodic complex Monge-Ampère measure",
  "title_text": "A Liouville theorem for plurisubharmonic functions with periodic complex Monge-Ampère measure",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9cr3rzhy3bvet",
  "venue": "arXiv",
  "versions": []
}