# Quasicircles modulo bilipschitz maps.

Revista Matemática Iberoamericana (2001)

- Volume: 17, Issue: 3, page 643-659
- ISSN: 0213-2230

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topRohde, 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 -

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