The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (962 KB) | Metadata | Table of Contents | ZAA summary
Volume 3, Issue 1, 1984, pp. 19–31
DOI: 10.4171/ZAA/88

Published online: 1984-02-29

Flächensätze für quasikonform fortsetzbare Abbildungen

Erich Hoy[1]

(1) Friedberg, Germany

In this paper an extension of the area principle to conformal mappings with a $Q_j$-quasiconformal continuation into the component $\mathcal B_j$ of the complement of a region $\mathcal G$ is given. A generalized area-theorem is proved for these mappings. The inequalities are sharp; the extrernal functions are connected with the solution of the equation $w_{\bar z} = \mu (z) \bar {w_z}$ with $\mu (z)$ being a piecewise constant function. These area theorems are applied to the estimations of the ranges of the coefficient for $z^{-1}$ of the Laurent expansion in the neighbourhood of infinity, the Schwarzian derivative and Golusin’s functional. Finally the possibility of an extension to conformal mappings with a quasiconformal continuation is shown. For Grunsky’s regions these inequalities are asymptotically sharp, if the restriction of the dilatation converges to a constant.

No keywords available for this article.

Hoy Erich: Flächensätze für quasikonform fortsetzbare Abbildungen. Z. Anal. Anwend. 3 (1984), 19-31. doi: 10.4171/ZAA/88