Geodesic
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

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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
Keywords: 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},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {113--154},
     publisher = {Springer Berlin Heidelberg},
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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

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