Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

Kari Astala, Tadeusz Iwaniec, István Prause, Eero Saksman

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.

ArXiv: 1303.2325