{
  "abstract": "We show that the map $u_*\\colon B_1\\subset\\mathbb R^3\\to\\mathbb S^2$, $x\\mapsto x/|x|$, minimizes the anisotropic energy \\begin{align*} \\int_{B_1} \\Big( k_1(\\mathrm{div}\\, u)^2+k_2 (u\\cdot \\mathrm{curl}\\, u)^2 +k_3 |u\\times\\mathrm{curl}\\, u|^2 \\Big) \\, dx, \\end{align*} among $\\mathbb S^2$-valued maps agreeing with it on the boundary, for values of $k_1,k_2,k_3>0$ beyond the known regime $k_1\\leq k_2$. Our main tool is a new stability estimate for $u_*$ as a minimizing sphere-valued harmonic map.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36972",
  "author_total": 2,
  "authors": [
    {
      "name": "Pierre Bousquet"
    },
    {
      "name": "Xavier Lamy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/86c77v57y5h0t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36972",
  "fulltext_url": null,
  "id": "86c77v57y5h0t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36972",
  "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",
      "2504|Liquid Crystal Research Advancements"
    ]
  ],
  "openalex": "W7214982849",
  "pdf_url": "https://arxiv.org/pdf/2609.36972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/86c77v57y5h0t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36972"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the minimality of the radial singularity in nematic liquid crystals",
  "title_text": "On the minimality of the radial singularity in nematic liquid crystals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/86c77v57y5h0t",
  "venue": "arXiv",
  "versions": []
}