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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
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