{
  "abstract": "In this paper we find a sufficient condition on an Ahlfors--David regular metric measure space under which it admits a partition into parts of prescribed measures and optimal (up to a constant) diameters. The proof uses the construction of dyadic cubes. The process is algorithmic: the pieces are cut out one by one via a filling procedure on the tree of dyadic cubes. We introduce the notion of spaces which admit a connected dyadic cube decomposition and prove that they admit a partition of the kind described above. We then develop several techniques to obtain such spaces and show some natural examples of this type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23867",
  "author_total": 1,
  "authors": [
    {
      "name": "Grigory Voinov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxgyh4zpawy40.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23867",
  "fulltext_url": null,
  "id": "dxgyh4zpawy40",
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  "landing_url": "https://arxiv.org/abs/2609.23867",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7214029150",
  "pdf_url": "https://arxiv.org/pdf/2609.23867",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxgyh4zpawy40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23867",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23867"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Optimal-diameter partitions into regions of the prescribed measure",
  "title_text": "Optimal-diameter partitions into regions of the prescribed measure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dxgyh4zpawy40",
  "venue": "arXiv",
  "versions": []
}