Illinois Journal of Mathematics

Bilipschitz homogeneous Jordan curves, Möbius maps, and dimension

David M. Freeman

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We characterize fractal chordarc curves in Euclidean space by the fact that they remain bilipschitz homogeneous under inversion. We illustrate this result by constructing two examples. The techniques used in these constructions provide a means of calculating various dimensions of bilipschitz homogeneous Jordan curves.

Article information

Illinois J. Math., Volume 54, Number 2 (2010), 753-770.

First available in Project Euclid: 14 October 2011

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Zentralblatt MATH identifier

Primary: 30C35: General theory of conformal mappings
Secondary: 51F99: None of the above, but in this section


Freeman, David M. Bilipschitz homogeneous Jordan curves, Möbius maps, and dimension. Illinois J. Math. 54 (2010), no. 2, 753--770. doi:10.1215/ijm/1318598680.

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