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

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this 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 ${\mathbb{R}}^3$, ${\text{bbS}}^3$ and ${\text{bbH}}^3$. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.