Acta Mathematica

, Volume 205, Issue 1, pp 189–197

Dimension of quasicircles

Article

DOI: 10.1007/s11511-010-0053-8

Cite this article as:
Smirnov, S. Acta Math (2010) 205: 189. doi:10.1007/s11511-010-0053-8

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

30C6230C80

Copyright information

© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Section de MathématiquesUniversité de GenèveGenève 4Switzerland