{
  "abstract": "For immersions of a closed $2h$-dimensional manifold $Σ$ into $\\mathbb R^m$, we consider curvature energies that are invariant under ambient isometries and dilations, with the principal term $\\int_Σ \\big|\\nabla^{(h-1)} \\vec{\\mathrm{I\\!I}}\\big|_g^2\\,d\\text{vol}_g$ and lower-order submanifold invariants. Following the four-dimensional approach developed in joint work with Bernard, Martino, and Rivière, we prove that every weak critical immersion in the natural Sobolev class $W^{h+1,2}$, whose induced metric and its inverse have $L^\\infty$ coefficients, is real-analytic in harmonic coordinates. The proof combines geometric conservation laws, structural identities, and elliptic estimates with critical Sobolev coefficients to obtain Morrey decay and bootstrap to full regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39606",
  "author_total": 1,
  "authors": [
    {
      "name": "Tian Lan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b88cxwmkhpr2v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39606",
  "fulltext_url": null,
  "id": "b88cxwmkhpr2v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39606",
  "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": "W7215047927",
  "pdf_url": "https://arxiv.org/pdf/2609.39606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b88cxwmkhpr2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.39606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regularity of critical immersions for scale-invariant curvature energies in even dimensions",
  "title_text": "Regularity of critical immersions for scale-invariant curvature energies in even dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/b88cxwmkhpr2v",
  "venue": "arXiv",
  "versions": []
}