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.
Original language | English (US) |
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Pages (from-to) | 207-213 |
Journal | Acta Mathematica Universitatis Comenianae |
Volume | 70 |
Issue number | 2 |
State | Published - 2001 |
Keywords
- hyperbolic radius
- hyperbolic metric
- convex functions