{
  "abstract": "Let $M^{n+1}$ be a complete Riemannian manifold with $\\sec_M\\ge-K_0$, $K_0\\ge0$, and let $\\mathfrak{F}$ be a codimension one foliation of $M$ by hypersurfaces of constant mean curvature, the constant depending on the leaf. We prove that the mean curvature of every leaf satisfies $|H|\\le(n+1)\\sqrt{K_0}$. In particular, the mean curvature of the leaves of a CMC foliation of a complete manifold with $|\\sec_M|\\le1$ is bounded by $n+1$, which answers positively a conjecture of Meeks III, Pérez, and Ros.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42093",
  "author_total": 2,
  "authors": [
    {
      "name": "José Edson Sampaio"
    },
    {
      "name": "Euripedes Carvalho da Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8153rj68j5tph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42093",
  "fulltext_url": null,
  "id": "8153rj68j5tph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42093",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8153rj68j5tph.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mean curvature bounds for CMC foliations of manifolds with sectional curvature bounded below",
  "title_text": "Mean curvature bounds for CMC foliations of manifolds with sectional curvature bounded below",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/8153rj68j5tph",
  "venue": "arXiv",
  "versions": []
}