, Volume 113, Issue 1, pp 265-291
Date: 17 Apr 2011

Modulus of curve families and extremality of spiral-stretch maps

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Abstract

We develop a method using the modulus of curve families to study minimisation problems for the mean distortion functional in the class of finite distortion homeomorphisms. We apply our method to prove extremality of the spiral-stretch mappings defined on annuli in the complex plane. This generalises results of Gutlyanskiĭ and Martio [12] and Strebel [23].

The authors were supported by Swiss National Science Foundation, European Research Council Project GALA and European Science Foundation Project HCAA