DOMAINS WITH CONVEX HYPERBOLIC RADIUS
L. V. Kovalev
Abstract.
The hyperbolic radius of a domain on the Riemann sphere is equal to the
reciprocal of the density of the hyperbolic metric. In the present paper, it is
proved that the hyperbolic radius is a convex function if and only if the
complement of the domain is a convex set.
Compressed Postscript 
