Dimension of quasicircles

Details Dimension of quasicircles Dimension of quasicircles

2009-04-07

arxiv.org/abs/0904.1237v1

Mathematics

Complex Variables

Acta Mathematica, to appear

Scientific paper

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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