{
  "abstract": "We prove an $\\varepsilon$-regularity theorem for $m$-varifolds with mean curvature in $L^p$, $p>m$, with respect to an anisotropic integrand satisfying a Michael-Simon inequality and the quadratic exposed condition: near sufficiently flat density-one points, such varifolds are representable as $C^{1,α}$ graphs. Combined with the recent proof of the anisotropic Michael-Simon inequality, this establishes an anisotropic Allard regularity theorem in arbitrary codimension for a large class of anisotropic integrands, including those close to the area functional. We also exhibit the first examples of anisotropies satisfying both the uniform scalar atomic condition and the Michael-Simon inequality, that are not close to any ellipsoidal norm. These include the $\\ell^q$ norms in every dimension and codimension, for explicit ranges of $q$, and a new class of axisymmetric anisotropies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20459",
  "author_total": 3,
  "authors": [
    {
      "name": "Antonio De Rosa"
    },
    {
      "name": "Benjy Firester"
    },
    {
      "name": "Raphael Tsiamis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dx0d13fnq1s1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20459",
  "fulltext_url": null,
  "id": "dx0d13fnq1s1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20459",
  "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": "W7213581220",
  "pdf_url": "https://arxiv.org/pdf/2609.20459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dx0d13fnq1s1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regularity of varifolds with bounded anisotropic first variation",
  "title_text": "Regularity of varifolds with bounded anisotropic first variation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/dx0d13fnq1s1v",
  "venue": "arXiv",
  "versions": []
}