Aleksandrov surfaces and hyperbolicity

Oh, Byung-Geun

doi:10.1090/S0002-9947-05-03977-2

Aleksandrov surfaces and hyperbolicity
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by Byung-Geun Oh

Trans. Amer. Math. Soc. 357 (2005), 4555-4577

DOI: https://doi.org/10.1090/S0002-9947-05-03977-2

Published electronically: June 10, 2005

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Abstract:

Aleksandrov surfaces are a generalization of two-dimensional Riemannian manifolds, and it is known that every open simply-connected Aleksandrov surface is conformally equivalent either to the unit disc (hyperbolic case) or to the plane (parabolic case). We prove a criterion for hyperbolicity of Aleksandrov surfaces which have nice tilings and where negative curvature dominates. We then apply this to generalize a result of Nevanlinna and give a partial answer for his conjecture about line complexes.

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