The Apollonian metric: limits of the comparison and bilipschitz properties
2003 ◽
Vol 2003
(20)
◽
pp. 1141-1158
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Keyword(s):
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.
2018 ◽
Vol 18
(4)
◽
pp. 717-722
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Keyword(s):
1997 ◽
Vol 49
(1)
◽
pp. 55-73
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2008 ◽
Vol 136
(09)
◽
pp. 3133-3143
◽
1987 ◽
Vol 8
(1-2)
◽
pp. 129-144
◽