Revista Matemática Iberoamericana

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Volume 28, Issue 3, 2012, pp. 603–630
DOI: 10.4171/RMI/687

Published online: 2012-07-16

Quasicircles and bounded turning circles modulo bi-Lipschitz maps

David A. Herron[1] and Daniel Meyer[2]

(1) University of Cincinnati, USA
(2) University of Helsinki, Finland

We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to bi-Lipschitz equivalence. This is a metric space analog of a result due to Rohde. Our construction also works for all bounded turning metric circles; these need not be doubling. As a byproduct, we show that a metric quasicircle with Assouad dimension strictly less than two is bi-Lipschitz equivalent to a planar quasicircle.

Keywords: Quasicircle, Jordan curve, bounded turning, doubling

Herron David, Meyer Daniel: Quasicircles and bounded turning circles modulo bi-Lipschitz maps. Rev. Mat. Iberoam. 28 (2012), 603-630. doi: 10.4171/RMI/687