JournalszaaVol. 21, No. 4pp. 1043–1054

Estimates for Quasiconformal Mappings onto Canonical Domains (II)

  • Vo Dang Thao

    National University, Hochiminh City, Vietnam
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Abstract

In this paper we establish estimates for normal K-quasiconformal mappings z=g(w)z = g(w) of any finitely-connected domain in the extended ww-plane onto the interior or exterior of the unit circle or the extended zz-plane with n(0)n (≥ 0) slits on the circles z=Rj(j=1,...,n)|z| = R_j (j = 1,...,n). The bounds in the estimates for Rj,g(w)R_j, |g(w)|, etc. are explicitly given. They are sharp or asymptotically sharp and deduced mainly from estimates for the inverse mappings of gg in our previous paper [10] based on Carleman’s and Gr¨otzsch’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