Acta Mathematica

, Volume 205, Issue 1, pp 189-197

First online:

Dimension of quasicircles

  • Stanislav SmirnovAffiliated withSection de Mathématiques, Université de Genève Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

2000 Math. Subject Classification

30C62 30C80