Illinois Journal of Mathematics

Mappings of finite distortion: gauge dimension of generalized quasicircles

David A. Herron and Pekka Koskela

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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

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

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C62: Quasiconformal mappings in the plane
Secondary: 28A78: Hausdorff and packing measures 30C65: Quasiconformal mappings in $R^n$ , other generalizations 31B15: Potentials and capacities, extremal length


Herron, David A.; Koskela, Pekka. Mappings of finite distortion: gauge dimension of generalized quasicircles. Illinois J. Math. 47 (2003), no. 4, 1243--1259.

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