Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

A theorem on the unitarizability of loop group valued monodromy representations is presented and applied to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply connected 3-dimensional space forms ³, ³ and ³. Additionally, the extended frame for any associated family of Delaunay surfaces is computed.