Astala's conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane

Abstract

Let be a compact set, be a K-quasiconformal map, and let 0 < t < 2. Let denote t-dimensional Hausdorff measure. Then This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala in [2] and answers in the positive a conjecture of K. Astala in op. cit. © 2010 Institut Mittag-Leffler.