# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332015

Acta Mathematica, 204, (2), 273-292, 2008.6
Let $E \subset \mathbb{C}$ be a compact set, $g:\mathbb{C} \to \mathbb{C}$ be a$K$-quasiconformal map, and let 0 <$t$< 2. Let ${\mathcal{H}^t}$ denote$t$-dimensional Hausdorff measure. Then $${\mathcal{H}^t}(E) = 0\quad \Rightarrow \quad {\mathcal{H}^{t'}}\left( {gE} \right) = 0,\quad t' = \frac{{2Kt}}{{2 + \left( {K - 1} \right)t}}.$$
Quasiconformal; Hausdorff measure; Removability
@inproceedings{michael2008astala’s,
title={Astala’s conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane},
author={Michael T. Lacey, Eric T. Sawyer, and Ignacio Uriarte-Tuero},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355038737724},
booktitle={Acta Mathematica},
volume={204},
number={2},
pages={273-292},
year={2008},
}

Michael T. Lacey, Eric T. Sawyer, and Ignacio Uriarte-Tuero. Astala’s conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane. 2008. Vol. 204. In Acta Mathematica. pp.273-292. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203355038737724.