{
  "abstract": "Let $M^n\\subset\\mathbb{S}^{n+1}(1)$ be a closed minimal hypersurface with constant $S=|h|^2$ and constant $f_3=\\operatorname{tr} h^3$, where $h$ is the shape operator. We prove that $S>n$ implies $S\\geq2n$, and that the equality images are precisely the minimal Cartan isoparametric hypersurfaces with three principal curvatures, which occur only in dimensions $n=3, 6, 12, 24$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27661",
  "author_total": 4,
  "authors": [
    {
      "name": "Jianquan Ge"
    },
    {
      "name": "Huixin Tan"
    },
    {
      "name": "Wenjiao Yan"
    },
    {
      "name": "Yunheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83t2nn5341f1h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27661",
  "fulltext_url": null,
  "id": "83t2nn5341f1h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27661",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214146353",
  "pdf_url": "https://arxiv.org/pdf/2609.27661",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83t2nn5341f1h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27661",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27661"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace",
  "title_text": "The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/83t2nn5341f1h",
  "venue": "arXiv",
  "versions": []
}