{
  "abstract": "A central conjecture in the regularity theory of harmonic maps asserts that the singular set of a stationary harmonic map has codimension at least three. In this paper, we construct counterexamples to this folklore conjecture. We construct stationary harmonic maps whose singular sets $S$ satisfies $\\dim S=n-2$ and $\\mathcal{H}^{n-2}(S)=0$ . The target is a smooth compact manifold diffeomorphic to $\\mathbb{S}^2 \\times \\mathbb{T}^3$, with metric arbitrarily close in $C^\\infty$ to the standard product metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21443",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenshuai Jiang"
    },
    {
      "name": "Chang Li"
    },
    {
      "name": "Wenyou Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d5xeeaefkqkhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21443",
  "fulltext_url": null,
  "id": "d5xeeaefkqkhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21443",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213949823",
  "pdf_url": "https://arxiv.org/pdf/2609.21443",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d5xeeaefkqkhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21443",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21443"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Prescribed singular sets for stationary harmonic maps",
  "title_text": "Prescribed singular sets for stationary harmonic maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/d5xeeaefkqkhz",
  "venue": "arXiv",
  "versions": []
}