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 language||English (US)|
|Journal||Acta Mathematica Universitatis Comenianae|
|State||Published - 2001|
- hyperbolic radius
- hyperbolic metric
- convex functions