Quasisymmetric graphs and Zygmund functions

Abstract

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

21 pages, no figures

References in corpus (3)

• Variation of quasiconformal mappings on lines
• Homeomorphic Solutions to Reduced Beltrami Equations
• On injectivity of quasiregular mappings