New constant mean curvature surfaces in the hyperbolic space

Abstract

Applying Ribaucour transformations, we construct two new 3-parameter families of complete surfaces, immersed in H3, with constant mean curvature 1 and infinitely many embedded horosphere type ends. Each surface of the first family is locally associated to an Enneper cousin. It has one irregular end and infinitely many regular ends asymptotic to horospheres. The surfaces of the second family are locally associated to a cateno id cousin. Each surface of this family has infinitely many embedded horosphere type ends and one regular end with infinite total curvature. © 2010 University of Illinois.