Domains with convex hyperbolic radius

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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.
Original languageEnglish (US)
Pages (from-to)207-213
JournalActa Mathematica Universitatis Comenianae
Issue number2
StatePublished - 2001


  • hyperbolic radius
  • hyperbolic metric
  • convex functions

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