Pointwise rotation for mappings with exponentially integrable distortion
HTML articles powered by AMS MathViewer
- by Lauri Hitruhin PDF
- Proc. Amer. Math. Soc. 144 (2016), 5183-5195 Request permission
Abstract:
We prove an upper bound for the pointwise rotation of mappings with $p$-exponentially integrable distortion. We also show that this bound is essentially optimal by providing examples which attain this rotation up to a constant multiplication.References
- Kari Astala, Tadeusz Iwaniec, and Gaven Martin, Elliptic partial differential equations and quasiconformal mappings in the plane, Princeton Mathematical Series, vol. 48, Princeton University Press, Princeton, NJ, 2009. MR 2472875
- Kari Astala, Tadeusz Iwaniec, István Prause, and Eero Saksman, Bilipschitz and quasiconformal rotation, stretching and multifractal spectra, Publ. Math. Inst. Hautes Études Sci. 121 (2015), 113–154. MR 3349832, DOI 10.1007/s10240-014-0065-6
- Zoltán M. Balogh, Katrin Fässler, and Ioannis D. Platis, Modulus of curve families and extremality of spiral-stretch maps, J. Anal. Math. 113 (2011), 265–291. MR 2788359, DOI 10.1007/s11854-011-0007-x
- Vladimir Gutlyanskiĭ and Olli Martio, Rotation estimates and spirals, Conform. Geom. Dyn. 5 (2001), 6–20. MR 1836404, DOI 10.1090/S1088-4173-01-00060-1
- David A. Herron and Pekka Koskela, Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math. 47 (2003), no. 4, 1243–1259. MR 2037001
- Fritz John, Rotation and strain, Comm. Pure Appl. Math. 14 (1961), 391–413. MR 138225, DOI 10.1002/cpa.3160140316
- Pekka Koskela and Jani Onninen, Mappings of finite distortion: capacity and modulus inequalities, J. Reine Angew. Math. 599 (2006), 1–26. MR 2279096, DOI 10.1515/CRELLE.2006.076
- Jani Onninen and Xiao Zhong, A note on mappings of finite distortion: the sharp modulus of continuity, Michigan Math. J. 53 (2005), no. 2, 329–335. MR 2152704, DOI 10.1307/mmj/1123090772
- Jussi Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Mathematics, Vol. 229, Springer-Verlag, Berlin-New York, 1971. MR 0454009
Additional Information
- Lauri Hitruhin
- Affiliation: Department of Mathematics and Statistics, P.O. Box 68, FIN-00014 University of Helsinki, Helsinki, Finland
- MR Author ID: 1173526
- Email: lauri.hitruhin@helsinki.fi
- Received by editor(s): December 23, 2015
- Received by editor(s) in revised form: February 2, 2016
- Published electronically: May 24, 2016
- Additional Notes: The author was financially supported by the Jenny and Antti Wihuri Foundation and by The Centre of Excellence in Analysis and Dynamics Research (Academy of Finland, decision 271983)
- Communicated by: Jeremy Tyson
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5183-5195
- MSC (2010): Primary 30C65
- DOI: https://doi.org/10.1090/proc/13155
- MathSciNet review: 3556263