The Distortion Theorem for quasiconformal mappings, Schottky’s Theorem and holomorphic motions

Martin, G.

doi:10.1090/S0002-9939-97-03677-0

The Distortion Theorem for quasiconformal mappings, Schottky’s Theorem and holomorphic motions
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Proc. Amer. Math. Soc. 125 (1997), 1095-1103 Request permission

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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