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 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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 
@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},
     year = {2015},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {121},
     doi = {10.1007/s10240-014-0065-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :