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 every metric quasicircle of Assouad dimension strictly less than two is bi-Lipschitz equivalent to a planar quasicircle.
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