Asian Journal of Mathematics

Volume 11 (2007)

Number 4

Monodromy of Constant Mean Curvature Surface in Hyperbolic Space

Pages: 651 – 670

DOI: http://dx.doi.org/10.4310/AJM.2007.v11.n4.a7

Author

Gian Pietro Pirola

Abstract

In this paper we give a global version of the Bryant representation of surfaces of constant mean curvature one (cmc-1 surfaces) 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.

Keywords

Monodromy; constant curvature; hyperbolic space

2010 Mathematics Subject Classification

58E15

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