## Einige neuere Entwicklungen bei quasikonformen Abbildungen. (Some new developments in quasi-conformal mappings).(German)Zbl 0758.30015

This interesting and important survey describes recent results on plane quasiconformal mappings which are close to the research interests of the author. The topics discussed cover a broad spectrum of results and in a pleasant manner extend the topics of an earlier survey [Jahresber. Dtsch. Math.-Ver. 90, No. 2, 90-109 (1988; Zbl 0638.30021)] of the same author. A sample of the contents follows: extremal problems for the class $$\Sigma(Q)$$, extension of a mapping by reflection over a Jordan curve, geometric applications of the reflection, physical applications to electrostatistics and connection to elliptic systems. Quadratic differentials play an important role in the proof of these results.

### MSC:

 30C62 Quasiconformal mappings in the complex plane 30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable

Zbl 0638.30021