Quasiconformal distortion of Hausdorff measures
Abstract
In this paper we prove that if f is a planar K-quasiconformal map and 0<t<2, t' = 2t/(2K-Kt+t), then f transforms sets of finite (t')-Hausdorff measure into sets of finite t-Hausdorff measure. We also prove the following more quantitative statement: If E is a planar set, then Ht(E) ≤ C(K) Ht'(f(E))t/(t'K), where Hs stands for the s-Hausdorff measure.
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