{
  "abstract": "Let $f$ be an upper semicontinuous function on a domain $Ω$, and let $V$ be the Perron envelope of $f$ formed only with subharmonic minorants that are bounded above on all of $Ω$. The usual argument for upper semicontinuity of Perron envelopes breaks down, since the regularization $V^*$ need not be bounded above; one only knows that $V=V^*$ outside a polar set. We show that nevertheless $V=V^*$ everywhere in $\\mathbb{R}^d$, using a local harmonic correction given by a Poisson integral on a ball. The plurisubharmonic analogue fails. We construct an explicit bounded B-regular Hartogs domain in $\\mathbb{C}^n$, $n\\geq2$, and a positive pluriharmonic function $W$ whose envelope of bounded-above plurisubharmonic minorants equals $W$ off an analytic disc and vanishes on it, although $W$ admits a positive plurisuperharmonic majorant $G$ with $W\\leq\\varepsilon G+C_\\varepsilon$ for all $\\varepsilon>0$. For pluriharmonic $W$, we show that the envelope recovers $W$ exactly on the union of the sets where such majorants are finite. The question arises in the study of quasibounded plurisubharmonic functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24139",
  "author_total": 1,
  "authors": [
    {
      "name": "Frank Wikström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6g28s54rvtn42.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24139",
  "fulltext_url": null,
  "id": "6g28s54rvtn42",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24139",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7171570105",
  "pdf_url": "https://arxiv.org/pdf/2607.24139",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6g28s54rvtn42.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2607.24139",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24139"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Perron envelopes with globally bounded minorants",
  "title_text": "Perron envelopes with globally bounded minorants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/6g28s54rvtn42",
  "venue": "arXiv",
  "versions": []
}