{
  "abstract": "Let $n\\ge5$ and $u$ be a positive singular solution of $Δ^2u=u^{(n+4)/(n-4)}$ in a punctured ball. A long-standing question is where or not $ -Δu>0$ in the punctured ball. In this paper we show that the answer is negative. More precisely we construct a positive singular solution whose singularity at the origin is nonremovable, while its lower limit there is zero. On a normal subspace, $-Δu$ converges to a strictly negative constant. The spherical minimum has order $r^β$, where $2<β<4$, and the spherical Harnack ratio is unbounded. The proof uses balanced planar polygons, finitely many exterior parameters and a countable gluing construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05998",
  "author_total": 3,
  "authors": [
    {
      "name": "Juncheng Wei"
    },
    {
      "name": "Hui Yang"
    },
    {
      "name": "Ronghao Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58pmfk0g06ty1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05998",
  "fulltext_url": null,
  "id": "58pmfk0g06ty1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05998",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05998",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58pmfk0g06ty1.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05998",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05998"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Failure of superharmonicity near an isolated singularity of the critical biharmonic equation",
  "title_text": "Failure of superharmonicity near an isolated singularity of the critical biharmonic equation",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/58pmfk0g06ty1",
  "venue": "arXiv",
  "versions": []
}