{
  "abstract": "In this article, we provide a complete answer to one of the most classical conjectures in differential geometry (of foliations). More precisely, we present a complete positive answer to the classical conjecture, due to Meeks III, Pérez, and Ros (2008), that states that every foliation on $\\mathbb{R}^{n+1}$ by (possibly varying) CMC hypersurfaces is a foliation by minimal hypersurfaces. Moreover, if $n\\leq 6$, such a CMC foliation must consist of parallel hyperplanes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20406",
  "author_total": 2,
  "authors": [
    {
      "name": "José Edson Sampaio"
    },
    {
      "name": "Euripedes Carvalho da Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq1f9876ynwc3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20406",
  "fulltext_url": null,
  "id": "eq1f9876ynwc3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20406",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7222237140",
  "pdf_url": "https://arxiv.org/pdf/2610.20406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq1f9876ynwc3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.20406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "CMC foliations on Euclidean spaces are minimal foliations",
  "title_text": "CMC foliations on Euclidean spaces are minimal foliations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/eq1f9876ynwc3",
  "venue": "arXiv",
  "versions": []
}