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Aleksandrov surfaces and hyperbolicity

Author: Byung-Geun Oh
Journal: Trans. Amer. Math. Soc. 357 (2005), 4555-4577
MSC (2000): Primary 30F20, 30D30; Secondary 28A75, 30D35
Published electronically: June 10, 2005
MathSciNet review: 2156721
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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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Additional Information

Byung-Geun Oh
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350

Received by editor(s): December 17, 2003
Published electronically: June 10, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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