Estimates for Quasiconformal Mappings onto Canonical Domains (II)

  • Vo Dang Thao

    National University, Hochiminh City, Vietnam

Abstract

In this paper we establish estimates for normal K-quasiconformal mappings of any finitely-connected domain in the extended -plane onto the interior or exterior of the unit circle or the extended -plane with slits on the circles . The bounds in the estimates for , etc. are explicitly given. They are sharp or asymptotically sharp and deduced mainly from estimates for the inverse mappings of in our previous paper [10] based on Carleman’s and Grötzsch’s inequalities and partly improved here. A generalization of the Schwarz lemma and improvements of some classical inequalities for conformal mappings are shown.

Cite this article

Vo Dang Thao, Estimates for Quasiconformal Mappings onto Canonical Domains (II). Z. Anal. Anwend. 21 (2002), no. 4, pp. 1043–1054

DOI 10.4171/ZAA/1125