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.
Kovalev, Leonid V. and Onninen, Jani, "Quasisymmetric Graphs and Zygmund Functions" (2011). Mathematics Faculty Scholarship. 55.
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