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

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

2006-08-26

arxiv.org/abs/math/0608651v1

Ann. della Scuola Norm. Sup. Pisa 5 (2006), 549-577

Mathematics

Differential Geometry

Scientific paper

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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