Some examples of Baker domains
  We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others. 
Walter Bergweiler, Jian-Hua Zheng
math.CV math.DS