Article

Acta Mathematica

, Volume 205, Issue 1, pp 189-197

Dimension of quasicircles

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

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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.

2000 Math. Subject Classification

30C62 30C80