Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
Astala, Kari1 ; Iwaniec, Tadeusz1, 2 ; Prause, István1 ; Saksman, Eero1
1 Department of Mathematics and Statistics, University of Helsinki P.O. Box 68 00014 Helsinki Finland
2 Department of Mathematics, Syracuse University 13244 Syracuse NY USA
Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 113-154.

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.

DOI : 10.1007/s10240-014-0065-6
Mots-clés : Hausdorff Dimension, Quasiconformal Mapping, Multifractal Spectrum, Beltrami Equation, Logarithmic Spiral
Astala, Kari 1 ; Iwaniec, Tadeusz 1, 2 ; Prause, István 1 ; Saksman, Eero 1

1 Department of Mathematics and Statistics, University of Helsinki P.O. Box 68 00014 Helsinki Finland
2 Department of Mathematics, Syracuse University 13244 Syracuse NY USA 
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     title = {Bilipschitz and quasiconformal rotation, stretching and multifractal spectra},
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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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