{
  "abstract": "We prove that the values set of \\(S=|A|^2\\) attained by closed embedded minimal hypersurfaces in \\(\\mathbb S^{n+1}(1)\\) with constant \\(S\\) and constant \\(f_3=\\operatorname{tr}(A^3)\\) is locally finite, where \\(A\\) denotes the shape operator. Neither the topology of the hypersurface nor the value of \\(f_3\\) is fixed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03711",
  "author_total": 4,
  "authors": [
    {
      "name": "Huixin Tan"
    },
    {
      "name": "Zizhou Tang"
    },
    {
      "name": "Yuquan Xie"
    },
    {
      "name": "Wenjiao Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8731qphvwpef7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03711",
  "fulltext_url": null,
  "id": "8731qphvwpef7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03711",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7208789024",
  "pdf_url": "https://arxiv.org/pdf/2609.03711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8731qphvwpef7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Chern's Conjecture with Constant Cubic Trace",
  "title_text": "Chern's Conjecture with Constant Cubic Trace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/8731qphvwpef7",
  "venue": "arXiv",
  "versions": []
}