Stretching and rotation sets of quasiconformal mappings

@article{Bongers2019StretchingAR,
title={Stretching and rotation sets of quasiconformal mappings},
author={Tyler Bongers},
year={2019}
}
• Tyler Bongers
• Published 12 October 2017
• Mathematics
• Annales Academiae Scientiarum Fennicae Mathematica
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion properties, and yield a flexible and powerful generalization of conformal mappings. In this work, we study the singularities of these maps, in particular the sizes of the sets where a quasiconformal map can exhibit given stretching and rotation behavior. We…
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References

SHOWING 1-10 OF 12 REFERENCES
On multifractal spectrum of quasiconformal mappings
which can be calculated to have stretch α and rotation γ at the origin along any sequence (rn). We can say, roughly speaking, that mapping f satisfies (1.1) at some point z if f stretches and rotates
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48)
• Mathematics
• 2009
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.
Sharp Examples for Planar Quasiconformal Distortion of Hausdorff Measures and Removability
In the celebrated paper [5, Acta Mathematica, 173, 1994], Astala showed optimal area distortion bounds and dimension distortion estimates for planar quasiconformal mappings. He asked (Question 4.4)
Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
• Mathematics
• 2015
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
Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
Acknowledgements Basic notation Introduction 1. General measure theory 2. Covering and differentiation 3. Invariant measures 4. Hausdorff measures and dimension 5. Other measures and dimensions 6.
Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane
• Mathematics
• 2010
<abstract abstract-type="TeX"><p> In this paper we prove the sharp distortion estimates for the quasiconformal mappings in the plane, both in terms of the Riesz capacities from nonlinear potential
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48
Thank you very much for reading elliptic partial differential equations and quasiconformal mappings in the plane pms 48. Maybe you have knowledge that, people have look numerous times for their
Function Spaces and Potential Theory
• Mathematics
• 1995
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge
Verdera: Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane. - Amer
• J. Math. 135:1,
• 2013
Function Spaces and Potential Theory, volume 314 of Grundlehren der mathematischen Wissenschaften
• 1996