{
  "abstract": "We prove that a local minimal hypersurface $M^3$ in the unit sphere $S^4$ with constant scalar curvature and three distinct principal curvatures at every point must be locally congruent to the minimal Cartan isoparametric hypersurface in $S^4$, which provides a positive answer to the Bryant conjecture \\cite{ChangLocal}. The key ingredient is to prove that, for each fixed \\(S_0>3\\), the set $\\mathscr{G}_{S_0}$ of fourth-order jets of normalized local graph solutions satisfying \\(|A|^2\\equiv S_0\\) is compact, where \\(A\\) denotes the shape operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00886",
  "author_total": 2,
  "authors": [
    {
      "name": "Chao Qian"
    },
    {
      "name": "Ya Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4y7g43cp08339.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00886",
  "fulltext_url": null,
  "id": "4y7g43cp08339",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00886",
  "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": "W7216439316",
  "pdf_url": "https://arxiv.org/pdf/2610.00886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4y7g43cp08339.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00886"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Bryant conjecture for minimal hypersurfaces in $S^4$",
  "title_text": "On the Bryant conjecture for minimal hypersurfaces in S^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/4y7g43cp08339",
  "venue": "arXiv",
  "versions": []
}