Simultaneous unitarizability of SLn(C)-valued maps, and constant mean curvature k-noid monodromy
W Rossman, N Schmitt
Abstract
We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SLn(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.
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