{
  "abstract": "Let $u\\in C^2(Ω)\\cap\\mathrm{PSH}(Ω)$ satisfy $(dd^c u)^2=0$ on a domain $Ω\\subset\\mathbb{C}^2$. We prove that the positive-rank locus of its Levi form carries a foliation by holomorphic curves tangent to the Levi-null directions, along which $u$ is harmonic. The flow boxes are locally bi-Lipschitz; in particular, the Levi-null slope is locally Lipschitz in the transverse variable. The Levi current is uniformly laminar on the positive-rank locus, with an explicit transverse measure, and laminar on $Ω$. A smooth example also shows that the Levi current can be laminar without being uniformly laminar on the whole domain. The analytic construction combines a local partial Legendre transform with a Hardy-space boundary equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28262",
  "author_total": 2,
  "authors": [
    {
      "name": "Yizhe Yang"
    },
    {
      "name": "Zhanpeng You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afdteyfyjxa3t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28262",
  "fulltext_url": null,
  "id": "afdteyfyjxa3t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28262",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223086774",
  "pdf_url": "https://arxiv.org/pdf/2610.28262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afdteyfyjxa3t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Foliations and Laminar Currents for $C^2$ Maximal Plurisubharmonic Functions",
  "title_text": "Foliations and Laminar Currents for C^2 Maximal Plurisubharmonic Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/afdteyfyjxa3t",
  "venue": "arXiv",
  "versions": []
}