The Carath\'{e}odory and Kobayashi/Royden Metrics by Way of Dual   Extremal Problems
  We study the Carath\'{e}odory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly incisive results are obtained for convex domains. 
Halsey Royden, Pit-Mann Wong, Steven G. Krantz
math.CV