Acta Mathematica

, Volume 205, Issue 1, pp 189–197

Dimension of quasicircles

Article

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+k2.

2000 Math. Subject Classification

30C62 30C80 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Section de MathématiquesUniversité de GenèveGenève 4Switzerland

Personalised recommendations