The Apollonian metric: limits of the comparison and bilipschitz properties
Hästö, Peter A.
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 1141-1158 / Harvested from Project Euclid
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The Apollonian metric is a generalization of the hyperbolic metric. It is defined in arbitrary domains in $\mathbb{R}^n$ . In this paper, we derive optimal comparison results between this metric and the $j_G$ 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.
Publié le : 2003-12-31
Classification:  30F45,  30C65 
@article{1073335211,
     author = {H\"ast\"o, Peter A.},
     title = {The Apollonian metric: limits of the comparison and bilipschitz
properties},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 1141-1158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1073335211}
}

Hästö, Peter A. The Apollonian metric: limits of the comparison and bilipschitz
properties. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  1141-1158. http://gdmltest.u-ga.fr/item/1073335211/