Dimension of quasicircles

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 .

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Veröffentlicht in:Acta mathematica 2010-09, Vol.205 (1), p.189-197
1. Verfasser: Smirnov, Stanislav
Format: Artikel
Sprache:eng
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Zusammenfassung: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 .
ISSN:0001-5962
1871-2509
DOI:10.1007/s11511-010-0053-8