  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.
