Dimension of quasicircles

Stanislav Smirnov

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arXiv · 0904.1237

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 $1+k^2$.

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Stanislav Smirnov. 2009-04-07. Dimension of quasicircles. https://arxiv.org/abs/0904.1237

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