New minimal surfaces in the hyperbolic space

Abstract

We obtain new complete minimal surfaces in the hyperbolic space H3, by using Ribaucour transformations. Starting with the family of spherical catenoids in H3 found by Mori (1981), we obtain 2- and 3-parameter families of new minimal surfaces in the hyperbolic space, by solving a non trivial integro-differential system. Special choices of the parameters provide minimal surfaces whose parametrizations are defined on connected regions of R2 minus a disjoint union of Jordan curves. Any connected region bounded by such a Jordan curve, generates a complete minimal surface, whose boundary at infinity of H3 is a closed curve. The geometric properties of the surfaces regarding the ends, completeness and symmetries are discussed.