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arXiv · 2609.27661

The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace

Jianquan Ge·Huixin Tan·Wenjiao Yan·Yunheng Zhang
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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 $n=3, 6, 12, 24$.

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Jianquan Ge, Huixin Tan, Wenjiao Yan, Yunheng Zhang. 2026-09-23. The Second Gap and Rigidity in Chern's Conjecture with Constant Cubic Trace. https://arxiv.org/abs/2609.27661

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