Positivity and completeness of invariant metrics
  We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of invariant metrics including the Bergman metric mainly for the unbounded domains. 
Taeyong Ahn, Herv\'e Gaussier, Kang-Tae Kim
math.CV