Asymptotic Conformality and Polygonal Approximation

Abstract

Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal maps. The paper provides an approximative characterization of local conformality and its connection with univalent polynomials. Also, some other quantitative applications of this connection are given.

Keywords

• univalent function
• quasiconformal extensions and reflections
• Grunsky and Teichmüller norms
• universal Teichmüller space
• hyperbolic metric
• generalized Gaussian curvature