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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)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Is there always a unique extremal Teichmüller mapping?
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by Kurt Strebel
Proc. Amer. Math. Soc. 90 (1984), 240-242
DOI: https://doi.org/10.1090/S0002-9939-1984-0727241-9

Abstract:

A boundary correspondence of the circumference of the unit disk, which can be continued quasiconformally to the disk and which has the following property, is constructed: If there exists a Teichmüller mapping which is associated to a holomorphic quadratic differential and which is extremal for the boundary correspondence, then there is more than one such mapping.
References
  • Kurt Strebel, Zur Frage der Eindeutigkeit extremaler quasikonformer Abbildungen des Einheitskreises. II, Comment. Math. Helv. 39 (1964), 77–89 (German). MR 176071, DOI 10.1007/BF02566945
  • Kurt Strebel, On lifts of extremal quasiconformal mappings, J. Analyse Math. 31 (1977), 191–203. MR 585316, DOI 10.1007/BF02813303
  • Lipman Bers, Quasiconformal mappings and Teichmüller’s theorem, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 89–119. MR 0114898
  • Olli Lehto, Group isomorphisms induced by quasiconformal mappings, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 241–244. MR 0367193
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Bibliographic Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 240-242
  • MSC: Primary 30C75; Secondary 30C60
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0727241-9
  • MathSciNet review: 727241