Quasisymmetric distortion spectrum

Abstract

We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the estimates remains an open question and is shown to be closely related to the fine structure of harmonic measure.

14 pages

Cited by in corpus (5)

• Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
• Asymptotic variance of the Beurling transform
• Quasicircles of dimension 1+k^2 do not exist
• Hausdorff measure of quasicircles
• Quasidisks and twisting of the Riemann map