Bounded geometry and characterization of some transcendental maps

@article{Keen2017BoundedGA,
  title={Bounded geometry and characterization of some transcendental maps},
  author={Linda Keen and Tao Chen and Yunping Jiang},
  journal={Indiana University Mathematics Journal},
  year={2017},
  volume={66},
  pages={1537-1571}
}
We define two classes of topological infinite degree covering maps modeled on two families of transcendental holomorphic maps. The first, which we call exponential maps of type (p, q), are branched coverings and is modeled on transcendental entire maps of the form Pe, where P and Q are polynomials of degrees p and q. The second is the class of universal covering maps from the plane to the sphere with two removed points modeled on transcendental meromorphic maps with two asymptotic values. The… 
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