Aleksandrov surfaces and hyperbolicity
Complex Variables
2014-12-15 v2
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(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.
Cite
@article{arxiv.math/0311054,
title = {Aleksandrov surfaces and hyperbolicity},
author = {Byung-Geun Oh},
journal= {arXiv preprint arXiv:math/0311054},
year = {2014}
}
Comments
23 pages; correction of minor misprints