arXiv 0907.49332009-07math.CAmath.FA

Quasiconformal distortion of Hausdorff measures

Xavier Tolsa

备注：: Minor corrections and one additional reference

英文摘要：

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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