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arXiv · 2609.22059

Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four

Zihao Wang
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Abstract

For every integer $d\ge4$, we prove strong stability for a subfamily of classical rotational hypersurfaces in $\mathbb H^d$ with normalized mean curvature one. The examples are complete, two-sided, properly embedded, and nowhere umbilic, with topology $\mathbb {R}\times\mathbb{S}^{d-2}$. An explicit positive supersolution yields a quantitative stability inequality for all compactly supported test functions. Consequently, endpoint horospherical rigidity fails in every ambient dimension at least four.

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Zihao Wang. 2026-09-18. Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four. https://arxiv.org/abs/2609.22059

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