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arXiv · 0907.4933

Quasiconformal distortion of Hausdorff measures

Xavier Tolsa
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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 H^t(E) \leq C(K) H^{t'}(f(E))^{t/(t'K)}, where H^s stands for the s-Hausdorff measure.

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Xavier Tolsa. 2009-09-09. Quasiconformal distortion of Hausdorff measures. https://arxiv.org/abs/0907.4933

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