Abstract
In this chapter we collect a number of geometric properties of surfaces which are modelled over the hyperbolic plane. The way of construction of these surfaces is cutting and pasting. For this we shall include surfaces with piece-wise geodesic boundary and prove existence and uniqueness theorems for geodesics in various types of homotopy classes. The chapter ends with an outline of the Fenchel-Nielsen parameters.
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© 2010 Springer Science+Business Media, LLC
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Buser, P. (2010). Hyperbolic Structures. In: Geometry and Spectra of Compact Riemann Surfaces. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4992-0_1
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DOI: https://doi.org/10.1007/978-0-8176-4992-0_1
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4991-3
Online ISBN: 978-0-8176-4992-0
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