- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
17
2001
3
Quasicircles modulo bilipschitz maps
Steffen
Rohde
University of Washington, SEATTLE, UNITED STATES
We give an explicit construction of all quasicircles , modulo bilipschitz maps . More precisely, we construct a class $\mathcal S$ of planar Jordan curves , using a process similar to the construction of the van Koch snowfl ake curve. These snowfl ake- like curves are easily seen to be quasicircles. We prove that for every quasicircle $\Gamma$ there is a bilipschitz homeomorphism $f$ of the plane and a snow flake- like curve $S \in \mathcal S$ with $\Gamma = f(S)$. In the same fashion we obtain a construction of all bilipschitz -homogeneous Jordan curves, modulo bilipschitz maps , and determine all dimension functions occuring for such curves. As a tool we construct a variant of the Konyagin- Volberg uniformly doubling measure on $\Gamma$.
General
643
659
10.4171/RMI/307
http://www.ems-ph.org/doi/10.4171/RMI/307