Simultaneous unitarizability of SL_n(C)-valued maps, and constant mean curvature k-noid monodromy

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 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.

References in corpus (1)

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