{
  "abstract": "In 1991, Laczkovich asked whether every measurable set of positive measure in $\\mathbb R^d$ can be mapped onto a cube with a Lipschitz map. We show that the answer is positive for every $d$. Our results also give a positive answer for Kolmogorov's problem on contractions onto polygons with small measure loss in the case of Jordan measurable sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38834",
  "author_total": 1,
  "authors": [
    {
      "name": "Attila Gáspár"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aemxmk7mbsgyf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38834",
  "fulltext_url": null,
  "id": "aemxmk7mbsgyf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38834",
  "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.MG"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38834",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aemxmk7mbsgyf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38834",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38834"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Solution of Laczkovich's Lipschitz mapping problem",
  "title_text": "Solution of Laczkovich's Lipschitz mapping problem",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/aemxmk7mbsgyf",
  "venue": "arXiv",
  "versions": []
}