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.