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2017 Inequalities and bi-Lipschitz conditions for the triangular ratio metric
Parisa Hariri, Matti Vuorinen, Xiaohui Zhang
Rocky Mountain J. Math. 47(4): 1121-1148 (2017). DOI: 10.1216/RMJ-2017-47-4-1121

Abstract

Let $G \subsetneq \mathbb {R}^n$ be a domain, and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally, we apply our results to study Lipschitz maps with respect to these metrics.

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Parisa Hariri. Matti Vuorinen. Xiaohui Zhang. "Inequalities and bi-Lipschitz conditions for the triangular ratio metric." Rocky Mountain J. Math. 47 (4) 1121 - 1148, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1121

Information

Published: 2017
First available in Project Euclid: 6 August 2017

zbMATH: 1376.30019
MathSciNet: MR3689948
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1121

Subjects:
Primary: 30C65, 51M10

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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