Quasicircles modulo bilipschitz maps.

Rohde, Steffen. "Quasicircles modulo bilipschitz maps.." Revista Matemática Iberoamericana 17.3 (2001): 643-659. <http://eudml.org/doc/39828>.

@article{Rohde2001,
abstract = {We give an explicit construction of all quasicircles, modulo bilipschitz maps. More precisely, we construct a class S of planar Jordan curves, using a process similar to the construction of the van Koch snowflake curve. These snowflake-like curves are easily seen to be quasicircles. We prove that for every quasicircle Γ there is a bilipschitz homeomorphism f of the plane and a snowflake-like curve S ∈ S with Γ = f(S). In the same fashion we obtain a construction of all bilipschitz-homogeneous Jordan curves, modulo bilipschitz maps, and determine all dimension functions occurring for such curves. As a tool, we construct a variant of the Konyagin-Volberg uniformly doubling measure on Γ.},
author = {Rohde, Steffen},
journal = {Revista Matemática Iberoamericana},
keywords = {Aplicaciones cuasiconformes; Homeomorfismos; Aplicación lipschitziana; quasicircles; snowflake curve},
language = {eng},
number = {3},
pages = {643-659},
title = {Quasicircles modulo bilipschitz maps.},
url = {http://eudml.org/doc/39828},
volume = {17},
year = {2001},
}

TY - JOUR
AU - Rohde, Steffen
TI - Quasicircles modulo bilipschitz maps.
JO - Revista Matemática Iberoamericana
PY - 2001
VL - 17
IS - 3
SP - 643
EP - 659
AB - We give an explicit construction of all quasicircles, modulo bilipschitz maps. More precisely, we construct a class S of planar Jordan curves, using a process similar to the construction of the van Koch snowflake curve. These snowflake-like curves are easily seen to be quasicircles. We prove that for every quasicircle Γ there is a bilipschitz homeomorphism f of the plane and a snowflake-like curve S ∈ S with Γ = f(S). In the same fashion we obtain a construction of all bilipschitz-homogeneous Jordan curves, modulo bilipschitz maps, and determine all dimension functions occurring for such curves. As a tool, we construct a variant of the Konyagin-Volberg uniformly doubling measure on Γ.
LA - eng
KW - Aplicaciones cuasiconformes; Homeomorfismos; Aplicación lipschitziana; quasicircles; snowflake curve
UR - http://eudml.org/doc/39828
ER -