{
  "abstract": "Let \\(X:M^3\\to\\RR^4\\) be a complete self-shrinker with constant squared norm \\(S\\) of the second fundamental form. We prove that \\(S=0\\) or \\(S=1\\), and that \\(X(M)\\) is isometric to a hyperplane or a standard product \\(\\SSS^k(\\sqrt{k})\\times\\RR^{3-k}\\), \\(1\\leq k\\leq3\\). This proves a conjecture proposed by Cheng and Wei for three-dimensional hypersurfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24964",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu Fu"
    },
    {
      "name": "Dan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72zzdm4qhzajq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24964",
  "fulltext_url": null,
  "id": "72zzdm4qhzajq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24964",
  "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": "W7223015867",
  "pdf_url": "https://arxiv.org/pdf/2610.24964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72zzdm4qhzajq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complete self-shrinkers with constant norm of the second fundamental form in \\(\\RR^4\\)",
  "title_text": "Complete self-shrinkers with constant norm of the second fundamental form in RR^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/72zzdm4qhzajq",
  "venue": "arXiv",
  "versions": []
}