{
  "abstract": "The Lipschitz-free space $\\mathcal{F}(M)$ is a canonical linearization of a complete metric space $M$ whose topological dual is the space of Lipschitz functions on $M$. We review the properties of $\\mathcal{F}(M)$ when the underlying space $M$ is purely 1-unrectifiable, that is, it contains no bi-Lipschitz copy of a subset of $\\mathbb{R}$ with positive measure. For compact $M$, this is equivalent to several Banach space properties of $\\mathcal{F}(M)$, including the Radon-Nikodým and Schur properties or admitting a predual. We shall see how the study of locally flat Lipschitz functions on $M$ reveals these equivalences, and describe a technique that allows most of them to be transferred to the non-compact setting. This manuscript is an expository text based on results by the author in collaboration with C. Gartland, C. Petitjean and A. Procházka, originally published in a Trans. Amer. Math. Soc. paper, and corresponds to a lecture delivered at the Second Winter School in Geometric Measure Theory at Westlake University, Hangzhou, on February 2026.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.02918",
  "author_total": 1,
  "authors": [
    {
      "name": "Ramón J. Aliaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/999jecksa9egn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02918",
  "fulltext_url": null,
  "id": "999jecksa9egn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02918",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7163366015",
  "pdf_url": "https://arxiv.org/pdf/2606.02918",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/999jecksa9egn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2606.02918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02918"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lipschitz-free spaces and purely 1-unrectifiable metric spaces",
  "title_text": "Lipschitz-free spaces and purely 1-unrectifiable metric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/999jecksa9egn",
  "venue": "arXiv",
  "versions": []
}