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Proceedings of the American Mathematical Society

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Shears for quasisymmetric maps


Author: Dragomir Šarić
Journal: Proc. Amer. Math. Soc. 149 (2021), 2487-2499
MSC (2020): Primary 30F45, 30F60
DOI: https://doi.org/10.1090/proc/15437
Published electronically: March 29, 2021
MathSciNet review: 4246800
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Abstract: We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family argument for quasisymmetric maps and some elementary hyperbolic geometry.


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Dragomir Šarić
Affiliation: Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, Room 4208, New York, New York 10016-4309; and Department of Mathematics, Queens College, The City University of New York, 237 Kiely Hall, 65-30 Kissena Blvd., Flushing, New York 11367
Email: Dragomir.Saric@qc.cuny.edu

Received by editor(s): April 6, 2020
Received by editor(s) in revised form: August 22, 2020
Published electronically: March 29, 2021
Communicated by: David Futer
Article copyright: © Copyright 2021 American Mathematical Society