Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

Abstract

We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal multifractal spectrum, based on new estimates for Burkholder functionals with complex parameters. As a consequence, we obtain optimal rotation estimates also for bi-Lipschitz maps.

Corrected typos, minor edits

Cited by in corpus (4)

• Asymptotic variance of the Beurling transform
• Quasidisks and twisting of the Riemann map
• The Orbits of Generalized Derivatives
• On asymptotically sharp bi-Lipschitz inequalities of quasiconformal mappings satisfying inhomogeneous polyharmonic equations