Quasisymmetric graphs and Zygmund functions

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 ${\mathrm{\Lambda }}_{\ast }$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.