{
  "abstract": "Let $M^n$, $n\\ge3$, be a closed oriented minimal hypersurface in the unit sphere with constant scalar curvature and constant $f_3=\\tr(h^3)$, where $h$ is the second fundamental form. We prove that $S=\\norm h^2>n$ implies $S\\ge2n$. Equality holds if and only if each connected component is locally congruent to a Cartan minimal isoparametric hypersurface with three distinct principal curvatures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26852",
  "author_total": 1,
  "authors": [
    {
      "name": "Shanlin Guan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0809sa7nb1be.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26852",
  "fulltext_url": null,
  "id": "c0809sa7nb1be",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26852",
  "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": "W7214224312",
  "pdf_url": "https://arxiv.org/pdf/2609.26852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0809sa7nb1be.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace",
  "title_text": "The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/c0809sa7nb1be",
  "venue": "arXiv",
  "versions": []
}