{
  "abstract": "Let $M^n$ be a closed minimal submanifold in the unit sphere $\\mathbb{S}^{n+q}$ with $n\\geqslant 3$ and $q\\geqslant 2$. Let $S$ be the squared length of its second fundamental form and $S_{\\max}=\\max_{p\\in M}S(p)$. We prove that if $M$ is not totally geodesic, then \\[ S_{\\max}>\\frac{2n}{3}+\\frac{n-2}{182}. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04631",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongwei Xu"
    },
    {
      "name": "Entao Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9j11x4q53d644.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04631",
  "fulltext_url": null,
  "id": "9j11x4q53d644",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04631",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7211878119",
  "pdf_url": "https://arxiv.org/pdf/2609.04631",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9j11x4q53d644.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04631",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04631"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The pinching constant for closed minimal submanifolds of high codimension in the sphere",
  "title_text": "The pinching constant for closed minimal submanifolds of high codimension in the sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9j11x4q53d644",
  "venue": "arXiv",
  "versions": []
}