The Distortion Theorem for Quasiconformal Mappings, Schottky’s Theorem and Holomorphic Motions
نویسنده
چکیده
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.
منابع مشابه
Stream lines, quasilines and holomorphic motions
1 Background The theory of holomorphic motions, introduced by Mané-Sad-Sullivan [1] and advanced by Slodkowski [2], has had a significant impact on the theory of quasiconformal mappings. A reasonably thorough account of this is given in our book [3]. In [4, 5] we established some classical distortion theorems for quasiconformal mappings and used the theory to develop connections between Schottk...
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