Nonuniqueness of Teichmüller extremal mappings

Reich, Edgar

doi:10.1090/S0002-9939-1983-0699424-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Nonuniqueness of Teichmüller extremal mappings
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by Edgar Reich PDF

Proc. Amer. Math. Soc. 88 (1983), 513-516 Request permission

Abstract:

A boundary correspondence for the unit disk is found with the following property. Among the extremal quasiconformal mappings of the disk with the specified boundary correspondence there are at least two Teichmüller mappings.

References

Eugen Blum, Die Extremalität gewisser Teichmüllerscher Abbildungen des Einheitskreises, Comment. Math. Helv. 44 (1969), 319–340 (German). MR 244476, DOI 10.1007/BF02564533
Kurt Strebel, Is there always a unique extremal Teichmüller mapping?, Proc. Amer. Math. Soc. 90 (1984), no. 2, 240–242. MR 727241, DOI 10.1090/S0002-9939-1984-0727241-9