Bergman and Caratheodory metrics of the Kohn-Nirenberg domains
  The Kohn-Nireberg domains are unbounded domains in the complex Euclidean space of dimension 2 upon which many outstanding questions are yet to be explored. The primary aim of this article is to demonstrate that the Bergman and Caratheodory metrics of any Kohn-Nirenberg domains are positive and complete. 
Taeyong Ahn, Herve Gaussier, Kang-Tae Kim
math.CV