{
  "abstract": "We prove mass estimates for PDE-constrained measures on sets of $σ$-finite ${\\mathcal H}^m$-measure, assuming an appropriate rank condition. As an application, we derive a Michael--Simon inequality for varifolds with bounded anisotropic first variation with respect to an integrand that satisfies the natural atomic condition (AC1).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34573",
  "author_total": 4,
  "authors": [
    {
      "name": "Guido De Philippis"
    },
    {
      "name": "Luca Gennaioli"
    },
    {
      "name": "Alessandro Pigati"
    },
    {
      "name": "Filip Rindler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c6e4fr8hymne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34573",
  "fulltext_url": null,
  "id": "4c6e4fr8hymne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34573",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214756716",
  "pdf_url": "https://arxiv.org/pdf/2609.34573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c6e4fr8hymne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34573"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality",
  "title_text": "Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4c6e4fr8hymne",
  "venue": "arXiv",
  "versions": []
}