, Volume 205, Issue 1, pp 189-197
Date: 20 Oct 2010

Dimension of quasicircles

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Abstract

We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k-quasicircle is at most 1+k 2.

This research was partially supported by the NSF grant DMS-9706875 as well as by the EU RTN CODY and Swiss NSF.