Quasiconformal distortion of Hausdorff measures
Classical Analysis and ODEs
2009-09-09 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0907.4933,
title = {Quasiconformal distortion of Hausdorff measures},
author = {Xavier Tolsa},
journal= {arXiv preprint arXiv:0907.4933},
year = {2009}
}
Comments
Minor corrections and one additional reference