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31 December 2003 The Apollonian metric: limits of the comparison and bilipschitz properties
Peter A. Hästö
Abstr. Appl. Anal. 2003(20): 1141-1158 (31 December 2003). DOI: 10.1155/S1085337503309042


The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains in n. In this paper, we derive optimal comparison results between this metric and the jG metric in a large class of domains. These results allow us to prove that Euclidean bilipschitz mappings have small Apollonian bilipschitz constants in a domain G if and only if G is a ball or half-space.


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Peter A. Hästö. "The Apollonian metric: limits of the comparison and bilipschitz properties." Abstr. Appl. Anal. 2003 (20) 1141 - 1158, 31 December 2003.


Published: 31 December 2003
First available in Project Euclid: 5 January 2004

zbMATH: 1067.30082
MathSciNet: MR2041216
Digital Object Identifier: 10.1155/S1085337503309042

Primary: 30C65 , 30F45

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 20 • 31 December 2003
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