Jordan domains and the universal Teichmüller space

Author:
Barbara Brown Flinn

Journal:
Trans. Amer. Math. Soc. **282** (1984), 603-610

MSC:
Primary 30C60; Secondary 30C35, 32G15

MathSciNet review:
732109

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Abstract: Let denote the lower half plane and let denote the Banach space of analytic functions in with , where is the suprenum over of the values . The universal Teichmüller space, , is the subset of consisting of the Schwarzian derivatives of conformal mappings of which have quasiconformal extensions to the extended plane. We denote by the set

**[1]**Lars V. Ahlfors,*Lectures on quasiconformal mappings*, Manuscript prepared with the assistance of Clifford J. Earle, Jr. Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. MR**0200442****[2]**A. F. Beardon and F. W. Gehring,*Schwarzian derivatives, the Poincaré metric and the kernel function*, Comment. Math. Helv.**55**(1980), no. 1, 50–64. MR**569245**, 10.1007/BF02566674**[3]**F. W. Gehring,*Univalent functions and the Schwarzian derivative*, Comment. Math. Helv.**52**(1977), no. 4, 561–572. MR**0457701****[4]**F. W. Gehring,*Spirals and the universal Teichmüller space*, Acta Math.**141**(1978), no. 1-2, 99–113. MR**0499134****[5]**O. Lehto and K. I. Virtanen,*Quasiconformal mappings in the plane*, 2nd ed., Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by K. W. Lucas; Die Grundlehren der mathematischen Wissenschaften, Band 126. MR**0344463****[6]**B. G. Osgood,*Univalence in multiply-connected domains*, Ph.D. Thesis, The University of Michigan, Ann Arbor, 1980.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1984-0732109-2

Keywords:
Schwarzian derivative,
quasicircle,
universal Teichmüller space

Article copyright:
© Copyright 1984
American Mathematical Society