Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

We establish sharp bounds for simultaneous local rotation and H"older-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.