Quasiconformal distortion of Hausdorff measures

Details Quasiconformal distortion of Hausdorff measures Quasiconformal distortion of Hausdorff measures

2009-07-28

arxiv.org/abs/0907.4933v2

Mathematics

Classical Analysis and ODEs

Minor corrections and one additional reference

Scientific paper

In this paper we prove that if f is a planar K-quasiconformal map and 0t' = 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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