{
  "abstract": "We give an alternative proof of a theorem of Brena, De Lellis and Franceschini (arXiv:2503.00649): the support of a stationary integral $d$ dimensional varifold in an open subset of $\\mathbf{R}^n$ is $(\\mathscr{H}^d, d)$ rectifiable of class $(k, α)$ for every positive integer $k$ and every $0 < α< 1$, and in particular of class $\\mathscr{C}^{\\infty}$. Our proof is independent of theirs and proceeds by different means. It compares the varifold, at every scale and at $\\mathscr{H}^d$ almost every point, with the graph of a solution of the Euler--Lagrange system of a smoothed area integrand, and thereby derives an excess-decay estimate that is faster than any power of the scale; the conclusion then follows from Santilli's characterisation of higher order rectifiability together with Whitney's extension theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19979",
  "author_total": 1,
  "authors": [
    {
      "name": "Sławomir Kolasiński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46843khmaj7nf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19979",
  "fulltext_url": null,
  "id": "46843khmaj7nf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19979",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213579897",
  "pdf_url": "https://arxiv.org/pdf/2609.19979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46843khmaj7nf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rectifiability of every finite order for stationary integral varifolds",
  "title_text": "Rectifiability of every finite order for stationary integral varifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/46843khmaj7nf",
  "venue": "arXiv",
  "versions": []
}