$S^{1}$-equivariant CMC-hypersurfaces in the Hyperbolic 3-space and the Corresponding Lagrangians

Abstract

A family of $S^{1}$-equivariant hypersurfaces of constant mean curvature can be obtained by using the Lagrangians with suitable potentials in the hyperbolic 3-space. The conservation law is effectively applied to the construction of $S^{1}$-equivariant hypersurfaces of constant mean curvature in the hyperbolic 3-space.