Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
Kari Astala, Tadeusz Iwaniec, Istv\'an Prause, Eero Saksman
TL;DR
This paper derives optimal bounds for local rotation and distortion in planar quasiconformal maps, providing new estimates for their multifractal spectra and extending results to bi-Lipschitz maps.
Contribution
It introduces sharp bounds for rotation and distortion in quasiconformal maps and develops new estimates for their multifractal spectra, advancing understanding of geometric function theory.
Findings
Sharp bounds for local rotation and H"older-distortion
New estimates for quasiconformal multifractal spectra
Optimal rotation bounds for bi-Lipschitz maps
Abstract
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.
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