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

W Rossman·N Schmitt
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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.

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W Rossman, N Schmitt. 2006-08-26. Simultaneous unitarizability of SL_n(C)-valued maps, and constant mean curvature k-noid monodromy. https://arxiv.org/abs/math/0608651

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