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

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

2004-03-22

arxiv.org/abs/math/0403366v3

J. London Math. Soc. (2) 75 (2007), 563-581.

Mathematics

Differential Geometry

18 pages, revised version

Scientific paper

10.1112/jlms/jdm005

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, $\bbS^3 $ and $\bbH^3$. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.

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