The Apollonian metric: the comparison property, bilipschitz mappings and thick sets

• Autorzy: Hästö P. A.
• Języki publikacji: EN

Abstrakty

EN

The Apollonian metric is a generalization of the hyperbolic metric to arbitrary open sets in Euclidean spaces. In this article we show that the Apollonian metric is comparable, to the jG metric in the set G if and only if its complement is unbounded and thick in the sense of Väisälä Vuorinen and Wallin [Thick sets and quasisymmetric maps, Nagoya Math. J. 135 (1994), 121-148] . These conditions are also equivalent to the following: there exists L > 1 such that all Euclidean L-bilipschitz mappings are Apollonian bilipschitz with uniformly bounded constant.

Słowa kluczowe

EN

Apollonian metric; Barbilian metric; bilipschitz mappings; quasiballs

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 2
• Strony: 209--232
• Opis fizyczny: Bibliogr. 40 poz.

Twórcy

autor

Hästö P. A.

• Department of Mathematics and Statistics University of Helsinki P. O. Box 68 FI-00014 Finland,

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