{
  "abstract": "Continuing our work in [Math. Ann. 392 (2025), 1503-1518], we construct new singular solutions to the complex Monge-Ampère equation with constant right-hand side in the Bedford-Taylor sense. Let $\\mathbb D$ denote the open unit disk in $\\mathbb C$. For $n\\geq 2$, these solutions include: (i) a bounded solution on $\\mathbb D^n$ that is discontinuous almost everywhere and nowhere classically differentiable; (ii) a continuous exhaustion of $\\mathbb C^n$ that does not belong to $W^{2,1}_{\\mathrm{loc}}(\\mathbb C^n)$; (iii) a continuous solution on $\\overline{\\mathbb D^n}$ whose Laplacian has a singular part. We construct these solutions from singular harmonic functions using partial Legendre transforms and holomorphic pullbacks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28606",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaxiang Wang"
    },
    {
      "name": "Wenlong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvnxc0g8kdw1b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28606",
  "fulltext_url": null,
  "id": "bvnxc0g8kdw1b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28606",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223082280",
  "pdf_url": "https://arxiv.org/pdf/2610.28606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvnxc0g8kdw1b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Singular solutions to the complex Monge-Ampère equation II",
  "title_text": "Singular solutions to the complex Monge-Ampère equation II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/bvnxc0g8kdw1b",
  "venue": "arXiv",
  "versions": []
}