The Apollonian metric: limits of the comparison and bilipschitzproperties

[摘要] The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains inℝn. In this paper, we derive optimal comparison results between this metric and thejGmetric in a large class of domains. These results allow us to prove that Euclidean bilipschitz mappings have small Apollonian bilipschitz constants in a domainGif and only ifGis a ball or half-space.

[学科分类] 数学（综合）