## Illinois Journal of Mathematics

### Mappings of finite distortion: gauge dimension of generalized quasicircles

#### Abstract

We determine the correct dimension gauge for measuring generalized quasicircles (the images of a circle under so-called $\mu$-homeomorphisms). We establish a sharp modulus of continuity estimate for the inverse of a homeomorphism with finite exponentially integrable distortion. We exhibit several illustrative examples.

#### Article information

Source
Illinois J. Math., Volume 47, Number 4 (2003), 1243-1259.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138102

Digital Object Identifier
doi:10.1215/ijm/1258138102

Mathematical Reviews number (MathSciNet)
MR2037001

Zentralblatt MATH identifier
1050.30012

#### Citation

Herron, David A.; Koskela, Pekka. Mappings of finite distortion: gauge dimension of generalized quasicircles. Illinois J. Math. 47 (2003), no. 4, 1243--1259. doi:10.1215/ijm/1258138102. https://projecteuclid.org/euclid.ijm/1258138102