The Apollonian metric: limits of the comparison and bilipschitz properties

Peter A. Hästö

Abstract and Applied Analysis, 2003, vol. 2003, issue 20, 1141-1158

Abstract: The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains in ℝn. 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.

Date: 2003
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https://doi.org/10.1155/S1085337503309042

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:20:p:1141-1158

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