{
  "abstract": "We prove that for every dimension $n \\geq 2$ and parameter $p \\in ]1,n[$, the hedgehog $u_0(x) = x/|x|$ is the unique minimiser of the $p$-energy $\\mathcal{E}_p [u]:=\\int_{\\mathbf{B}^n}|\\nabla u|^p\\,{\\rm d}x$ in the class of $W^{1,p}$-mappings from the $n$-dimensional unit ball $\\mathbf{B}^n$ to the $(n-1)$-dimensional unit sphere $\\mathbf{S}^{n-1}=\\partial\\mathbf{B}^n$ whose trace equal to the identity on $\\mathbf{S}^{n-1}$. This answers in the affirmative an open question on p.29 in [Robert M. Hardt, Singularities of harmonic maps, Bull. Amer. Math. Soc. (N.S.) 34 (1997), 15--34].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13979",
  "author_total": 1,
  "authors": [
    {
      "name": "Siran Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvsh6kjdwnht5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13979",
  "fulltext_url": null,
  "id": "fvsh6kjdwnht5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13979",
  "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": "W7213326067",
  "pdf_url": "https://arxiv.org/pdf/2609.13979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvsh6kjdwnht5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The hedgehog uniquely minimises every $p$-energy",
  "title_text": "The hedgehog uniquely minimises every p-energy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fvsh6kjdwnht5",
  "venue": "arXiv",
  "versions": []
}