{
  "abstract": "We give a self-contained exposition of metric differentiability for Lipschitz mappings from sets in Euclidean spaces into arbitrary metric spaces, together with the corresponding area and co-area formulas. The novelty is a new metric implicit function theorem for mappings into metric spaces, which is then used to give a direct and geometric proof of the co-area formula for Lipschitz mappings into metric spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09121",
  "author_total": 3,
  "authors": [
    {
      "name": "Behnam Esmayli"
    },
    {
      "name": "Paweł Goldstein"
    },
    {
      "name": "Piotr Hajłasz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/358dbjyr64nbs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09121",
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  "id": "358dbjyr64nbs",
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  "landing_url": "https://arxiv.org/abs/2609.09121",
  "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"
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      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7212006798",
  "pdf_url": "https://arxiv.org/pdf/2609.09121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/358dbjyr64nbs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas",
  "title_text": "Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/358dbjyr64nbs",
  "venue": "arXiv",
  "versions": []
}