Open Access
2010 Dimension of quasicircles
Stanislav Smirnov
Author Affiliations +
Acta Math. 205(1): 189-197 (2010). DOI: 10.1007/s11511-010-0053-8


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.

Funding Statement

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


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Stanislav Smirnov. "Dimension of quasicircles." Acta Math. 205 (1) 189 - 197, 2010.


Received: 24 October 2008; Published: 2010
First available in Project Euclid: 31 January 2017

zbMATH: 1211.30037
MathSciNet: MR2736155
Digital Object Identifier: 10.1007/s11511-010-0053-8

Primary: 30C62
Secondary: 30C80

Rights: 2010 © Institut Mittag-Leffler

Vol.205 • No. 1 • 2010
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