Quasisymmetric graphs and Zygmund functions

Details Quasisymmetric graphs and Zygmund functions Quasisymmetric graphs and Zygmund functions

2011-07-12

arxiv.org/abs/1107.2435v1

Mathematics

Complex Variables

21 pages, no figures

Scientific paper

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.

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