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.
@article{PMIHES_2015__121__113_0, author = {Astala, Kari and Iwaniec, Tadeusz and Prause, Istv\'an and Saksman, Eero}, title = {Bilipschitz and quasiconformal rotation, stretching and multifractal spectra}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {113--154}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {121}, year = {2015}, doi = {10.1007/s10240-014-0065-6}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-014-0065-6/} }
TY - JOUR AU - Astala, Kari AU - Iwaniec, Tadeusz AU - Prause, István AU - Saksman, Eero TI - Bilipschitz and quasiconformal rotation, stretching and multifractal spectra JO - Publications Mathématiques de l'IHÉS PY - 2015 SP - 113 EP - 154 VL - 121 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-014-0065-6/ DO - 10.1007/s10240-014-0065-6 LA - en ID - PMIHES_2015__121__113_0 ER -
%0 Journal Article %A Astala, Kari %A Iwaniec, Tadeusz %A Prause, István %A Saksman, Eero %T Bilipschitz and quasiconformal rotation, stretching and multifractal spectra %J Publications Mathématiques de l'IHÉS %D 2015 %P 113-154 %V 121 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-014-0065-6/ %R 10.1007/s10240-014-0065-6 %G en %F PMIHES_2015__121__113_0
Astala, Kari; Iwaniec, Tadeusz; Prause, István; Saksman, Eero. Bilipschitz and quasiconformal rotation, stretching and multifractal spectra. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 113-154. doi : 10.1007/s10240-014-0065-6. http://www.numdam.org/articles/10.1007/s10240-014-0065-6/
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