{
  "abstract": "We generalize Moser's stability theorem for minimal hypersurface foliations to arbitrary codimension. Let $\\mathbb{T}^N=\\mathbb{R}^N/\\mathbb{Z}^N$ be the standard torus, and let $P\\subset\\mathbb{R}^N$ be an $m$-plane satisfying a Diophantine condition relative to $\\mathbb{Z}^N$. We prove that, under every sufficiently small smooth $\\mathbb{Z}^N$-periodic perturbation of the Euclidean metric, the affine foliation of $\\mathbb{T}^N$ induced by $P$ persists as a smoothly conjugate foliation by minimal $m$-dimensional submanifolds. The normalized conjugating displacement depends smoothly and tamely on the metric and is locally unique. The proof uses Hamilton's formulation of the Nash-Moser implicit function theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15984",
  "author_total": 1,
  "authors": [
    {
      "name": "Hoan Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90t72hs4h4859.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15984",
  "fulltext_url": null,
  "id": "90t72hs4h4859",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15984",
  "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.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221762068",
  "pdf_url": "https://arxiv.org/pdf/2610.15984",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90t72hs4h4859.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15984",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15984"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stability of Diophantine Minimal Foliations in Arbitrary Codimension",
  "title_text": "Stability of Diophantine Minimal Foliations in Arbitrary Codimension",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/90t72hs4h4859",
  "venue": "arXiv",
  "versions": []
}