Title: Finding complete conformal metrics to extend conformal mappings

Authors: M. Chuaqui and B. Osgood

Issue: Volume 47 (1998), Issue 4, 1273-1292

Abstract: This paper shows how new differential geometric approaches to univalence criteria involving the Schwarzian derivative can be applied to a classical, but very general, criterion of Nehari. We show how positive solutions to the second order ODE associated to the Schwarzian can be used to construct complete conformal metrics. These lead to explicit formulas for homeomorphic and quasiconformal extensions of conformal mappings as generalizations of the Ahlfors-Weill extension.