  We give necessary and sufficient local conditions for the simultaneous
unitarizability of a set of analytic matrix maps from an analytic 1-manifold
into SL_n(C) under conjugation by a single analytic matrix map. We apply this
result to the monodromy arising from an integrable partial differential
equation to construct a family of k-noids, genus-zero constant mean curvature
surfaces with three or more ends in Euclidean, spherical and hyperbolic
3-spaces.
