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Proceedings of the American Mathematical Society

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The Distortion Theorem
for Quasiconformal Mappings,
Schottky's Theorem and Holomorphic Motions

Author: G. J. Martin
Journal: Proc. Amer. Math. Soc. 125 (1997), 1095-1103
MSC (1991): Primary 30C60
MathSciNet review: 1363178
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Abstract: We prove the equivalence of Schottky's theorem and the distortion theorem for planar quasiconformal mappings via the theory of holomorphic motions. The ideas lead to new methods in the study of distortion theorems for quasiconformal mappings and a new proof of Teichmüller's distortion theorem.

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Additional Information

G. J. Martin
Affiliation: Department of Mathematics, Australian National University, Canberra, ACT, Australia

Received by editor(s): March 20, 1995
Received by editor(s) in revised form: September 28, 1995
Additional Notes: This research was supported in part by grants from the New Zealand Foundation for Research, Science and Technology and the Australian Research Council.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1997 American Mathematical Society