Bifurcations of immersed constant mean curvature hypersurfaces in hyperbolic space (Q376732)

In an earlier paper [Acta Math. Sci., Ser. B, Engl. Ed. 33, No. 3, 830--838 (2013; Zbl 1299.53128)], given \(H>1\), the author has shown the existence of a one-parameter family of constant-curvature \(H\) hypersurfaces of revolution in the hyperbolic space \(\mathbb H^{n+1}\). Here, he shows existence of a smooth branch of such hypersurfaces which are invariant under the action of the group \(\{ \pm I\}\times\mathrm{O}(n-1)\times\mathrm{O}(1)\) which branch from a surface of the previously defined family.