Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps
Complex Variables
2012-10-23 v2 Metric Geometry
Abstract
We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to \bl\ 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
Cite
@article{arxiv.1006.2929,
title = {Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps},
author = {David A. Herron and Daniel Meyer},
journal= {arXiv preprint arXiv:1006.2929},
year = {2012}
}
Comments
30 pages, 3 figures, to appear in Rev. Mat. Iberoamericana