{
  "abstract": "We prove that, in every dimension, the relative Euclidean isoperimetric profile of the unit cube equals one whenever the prescribed volume differs from one half by at most $6.25\\times10^{-12}$. The only minimizers in this interval are coordinate slabs. This answers Glaudo's question on the existence of a dimension-free central plateau. The proof combines a dimension-free local optimality estimate for slabs, established through BV slicing and a small-support estimate, with a quantitative Gaussian rigidity argument that forces the normal of an approximating half-space to be close to a coordinate direction.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18351",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8t50razae1m3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18351",
  "fulltext_url": null,
  "id": "f8t50razae1m3",
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  "landing_url": "https://arxiv.org/abs/2610.18351",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7221810406",
  "pdf_url": "https://arxiv.org/pdf/2610.18351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8t50razae1m3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An explicit dimension-free isoperimetric plateau in the cube",
  "title_text": "An explicit dimension-free isoperimetric plateau in the cube",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/f8t50razae1m3",
  "venue": "arXiv",
  "versions": []
}