---
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.'
address:
- 'Department of Mathematics, University of Cincinnati, OH 45221'
- 'Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hällströmin katu 2b) FI-00014, Helsinki, Finland'
author:
- David A Herron
- Daniel Meyer
bibliography:
- 'mrabbrev.bib'
- 'bib.bib'
title: 'Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps'
---

[^1]

[^1]: The first author was partially supported by the Charles Phelps Taft Research Center. The second author was supported by the Academy of Finland, projects SA-134757 and SA-118634.
