An analogue of the UP-iteration for constant mean curvature one surfaces in hyperbolic 3-space

The UP-iteration is a method for constructing new rational minimal surfaces of genus zero from a given rational minimal surface. Here, an analogue of the UP-iteration is given for constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space H^3. This yields countably many new complete CMC-1 surfaces of finite total curvature in H^3, which admit isometric deformations preserving principal curvatures.