Aleksandrov surfaces and hyperbolicity

Details Aleksandrov surfaces and hyperbolicity Aleksandrov surfaces and hyperbolicity

2003-11-05

arxiv.org/abs/math/0311054v2

Mathematics

Complex Variables

23 pages; correction of minor misprints

Scientific paper

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(triangulations) 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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