Acta Mathematica

Dimension of quasicircles

Stanislav Smirnov

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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.


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

Article information

Acta Math. Volume 205, Number 1 (2010), 189-197.

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

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Zentralblatt MATH identifier

Primary: 30C62: Quasiconformal mappings in the plane
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

2010 © Institut Mittag-Leffler


Smirnov, Stanislav. Dimension of quasicircles. Acta Math. 205 (2010), no. 1, 189--197. doi:10.1007/s11511-010-0053-8.

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