Acta Mathematica

Dimension of quasicircles

Stanislav Smirnov

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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+k2.

Note

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

Article information

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

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

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485892485

Digital Object Identifier
doi:10.1007/s11511-010-0053-8

Zentralblatt MATH identifier
1211.30037

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

Rights
2010 © Institut Mittag-Leffler

Citation

Smirnov, Stanislav. Dimension of quasicircles. Acta Math. 205 (2010), no. 1, 189--197. doi:10.1007/s11511-010-0053-8. http://projecteuclid.org/euclid.acta/1485892485.


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References

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