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