Bounded Geometry and Families of Meromorphic Functions with Two   Asymptotic Values
  In this paper we consider the topological class, denoted by AV2, of universal covering maps from the plane to the sphere with two removed points. We prove that an element f in AV2 with finite post-singular set is combinatorially equivalent to a meromorphic transcendental map g with constant Schwarzian derivative if any only if f satisfies a Bounded Geometry condition. 
Tao Chen, Yunping Jiang and Linda Keen
math.DS math.CV