Quasidisks and twisting of the Riemann map

Abstract

Consider a conformal map from the unit disk onto a quasidisk. We determine a range of critical complex powers with respect to which the derivative is integrable. The results fit into the picture predicted by a circular analogue of Brennan's conjecture.

18 pages, 1 figure

References in corpus (4)

• Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
• The three point Pick problem on the Bidisk
• Asymptotic variance of the Beurling transform
• Quasicircles of dimension 1+k^2 do not exist