JournalsrmiVol. 28, No. 3pp. 603–630

Quasicircles and bounded turning circles modulo bi-Lipschitz maps

  • David A. Herron

    University of Cincinnati, USA
  • Daniel Meyer

    University of Helsinki, Finland
Quasicircles and bounded turning circles  modulo bi-Lipschitz maps cover
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Abstract

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.

Cite this article

David A. Herron, Daniel Meyer, Quasicircles and bounded turning circles modulo bi-Lipschitz maps. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 603–630

DOI 10.4171/RMI/687