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 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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
. |
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ISSN: | 0001-5962 1871-2509 |
DOI: | 10.1007/s11511-010-0053-8 |