Pointwise rotation for mappings with exponentially integrable distortion

Hitruhin, Lauri

doi:10.1090/proc/13155

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