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PreprintCC BY 4.0arXiv

The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace

  • Shanlin Guan
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Abstract

Let Mn, n≥3, be a closed oriented minimal hypersurface in the unit sphere with constant scalar curvature and constant f3=tr(h3), where h is the second fundamental form. We prove that S=norm h2>n implies S≥2n. Equality holds if and only if each connected component is locally congruent to a Cartan minimal isoparametric hypersurface with three distinct principal curvatures.

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Cite

BibTeXRIS
BibTeX
@misc{guan2026second,
  title = {{The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace}},
  author = {Shanlin Guan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26852},
  eprint = {2609.26852},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26852},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace
AU  - Shanlin Guan
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26852
UR  - https://arxiv.org/abs/2609.26852
AB  - Let M^n, n≥3, 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≥2n. Equality holds if and only if each connected component is locally congruent to a Cartan minimal isoparametric hypersurface with three distinct principal curvatures.
ER  -