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

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.

Funding Statement

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

Citation

Download Citation

Stanislav Smirnov. "Dimension of quasicircles." Acta Math. 205 (1) 189 - 197, 2010. https://doi.org/10.1007/s11511-010-0053-8

Information

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

Subjects:
Primary: 30C62
Secondary: 30C80

Rights: 2010 © Institut Mittag-Leffler

JOURNAL ARTICLE
9 PAGES


SHARE
Vol.205 • No. 1 • 2010
Back to Top