Free boundary CMC annuli in spherical and hyperbolic balls

We construct, for any H∈ R, infinitely many free boundary annuli in geodesic balls of S³ with constant mean curvature H and a discrete, non-rotational, symmetry group. Some of these free boundary CMC annuli are actually embedded if H≥ 1/√3. We also construct embedded, non-rotational, free boundary CMC annuli in geodesic balls of H³, for all values $H>1$ of the mean curvature H.