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arXiv · 2609.26852

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

Shanlin Guan
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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.

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Shanlin Guan. 2026-09-22. The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace. https://arxiv.org/abs/2609.26852

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