Monodromy of constant mean curvature surface in hyperbolic space

Details Monodromy of constant mean curvature surface in hyperbolic space Monodromy of constant mean curvature surface in hyperbolic space

2006-11-20

arxiv.org/abs/math/0611611v1

Mathematics

Differential Geometry

22 pages, to appear in The Asian Journal of Mathematics

Scientific paper

We give a global version of the Bryant representation of surfaces of constant
mean curvature one (cmc-1) in hyperbolic space. This allows to set the
associated non-abelian period problem in the framework of flat unitary vector
bundles on Riemann surfaces. We use this machinery to prove the existence of
certain cmc-1 surfaces having prescribed global monodromy.

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