Free boundary CMC annuli in spherical and hyperbolic balls

We construct, for any $H\in \mathbb{R}$, infinitely many free boundary annuli in geodesic balls of ${\mathbb{S}}^3$ with constant mean curvature $H$ and a discrete, non-rotational, symmetry group. Some of these free boundary CMC annuli are actually embedded if $H\ge 1\mathrm{/}\sqrt{3}$. We also construct embedded, non-rotational, free boundary CMC annuli in geodesic balls of ${\mathbb{H}}^3$, for all values $H>1$ of the mean curvature $H$.