A New Weighted Metric: the Relative Metric II

Details A New Weighted Metric: the Relative Metric II A New Weighted Metric: the Relative Metric II

2001-08-03

arxiv.org/abs/math/0108026v2

Mathematics

Metric Geometry

23 pages, 2 figures

Scientific paper

In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.

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