{
  "abstract": "For every $2\\le m\\le n$, we construct Hölder continuous functions on the closed unit ball that are minimal in the Cegrell class $\\F_m$, although their Hessian measures are not maximal in the $m$-subharmonic ordering. This answers a question posed by the second author. We also obtain a minimality criterion based on partial pluricomplex energy and an explicit family of Monge--Ampère examples on a product domain. For $m=1$, minimality and maximality are equivalent on a ball.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30926",
  "author_total": 2,
  "authors": [
    {
      "name": "Thai Duong Do"
    },
    {
      "name": "Van Thien Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fr8fgxq2r0twm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30926",
  "fulltext_url": null,
  "id": "fr8fgxq2r0twm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30926",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214659660",
  "pdf_url": "https://arxiv.org/pdf/2609.30926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fr8fgxq2r0twm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30926"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Minimal m-subharmonic functions with nonmaximal Hessian measures",
  "title_text": "Minimal m-subharmonic functions with nonmaximal Hessian measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/fr8fgxq2r0twm",
  "venue": "arXiv",
  "versions": []
}