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- Title
Hilbert Metric in the Unit Ball.
- Authors
Rainio, Oona; Vuorinen, Matti
- Abstract
The Hilbert metric between two points , in a bounded convex domain is defined as the logarithm of the cross-ratio , and the intersection points of the Euclidean line passing through the points , and the boundary of the domain. Here, we study this metric in the case of the unit ball . We present an identity between the Hilbert metric and the hyperbolic metric, give several inequalities for the Hilbert metric, and results related to the inclusion properties of the balls defined in the Hilbert metric. Furthermore, we study the distortion of the Hilbert metric under conformal and quasiregular mappings.
- Subjects
UNIT ball (Mathematics); QUASICONFORMAL mappings; CONFORMAL mapping; CONVEX domains; LOGARITHMS
- Publication
Studia Scientiarum Mathematicarum Hungarica, 2023, Vol 60, Issue 2/3, p175
- ISSN
0081-6906
- Publication type
Article
- DOI
10.1556/012.2023.01544