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Is there always a unique extremal Teichmüller mapping?

Author: Kurt Strebel
Journal: Proc. Amer. Math. Soc. 90 (1984), 240-242
MSC: Primary 30C75; Secondary 30C60
MathSciNet review: 727241
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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.

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  • [2] -, On lifts of extremal quasiconformal mappings, J. Analyse Math. 31 (1977), 191-203. MR 0585316 (58:28489)
  • [3] L. Bers. Quasiconformal mappings and Teichmüller's theorem, Analytic Functions (R. Nevanlinna et al., eds.), Princeton Univ. Press, Princeton, N. J., 1960, pp. 89-119. MR 0114898 (22:5716)
  • [4] O. Lehto, Group isomorphisms induced by quasiconformal mappings, Contributions to Analysis, Academic Press, New York, 1974, pp. 241-244. MR 0367193 (51:3435)

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