JP Journal of Geometry and Topology
Volume 7, Issue 1, Pages 23 - 44
(March 2007)
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WEAK METRICS ON EUCLIDEAN DOMAINS
Athanase Papadopoulos (France) and Marc Troyanov (Switzerland)
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Abstract:
A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. The aim of this paper is to present some interesting weak metrics and to study some of their properties. In particular, we introduce a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. We relate this weak metric to some familiar metrics such as the Poincaré metric, the Klein-Hilbert metric, the Funk metric and the part metric which all play important roles in classical and in recent work on geometric function theory. |
| Keywords and phrases: weak metric, Apollonian weak metric, hyperbolic geometry, Poincaré model, Klein model, Klein-Hilbert metric, Funk weak metric, part metric, Poincaré metric, Apollonian semi-metric, half-Apollonian semi-metric. |
| Communicated by Bruno Colbois |
| Number of Downloads: 322 | Number of Views: 1125 |
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