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arXiv · 2609.34283

Stable Constant Mean Curvature Hypersurfaces in $\mathbb{H}^n$

Filippo Gaia·Rafe Mazzeo·Ivan Miranda
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Abstract

For every $n\geq 4$ and every $H$ in a neighborhood of $n-1$ (depending on $n$), we prove the existence of a properly embedded strongly stable CMC hypersurface in $\mathbb H^n$ with mean curvature $H$ and infinitely many ends, invariant under the action of a Schottky group. In particular, stable Bernstein-type rigidity fails in this range.

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Filippo Gaia, Rafe Mazzeo, Ivan Miranda. 2026-09-28. Stable Constant Mean Curvature Hypersurfaces in $\mathbb{H}^n$. https://arxiv.org/abs/2609.34283

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