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A New Weighted Metric: the Relative Metric II

Peter A. Hasto
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Abstract

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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Peter A. Hasto. 2001-09-03. A New Weighted Metric: the Relative Metric II. https://arxiv.org/abs/math/0108026

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