The argument of an extremal dilatation

Ortel, Marvin; Smith, Wayne

doi:10.1090/S0002-9939-1988-0962819-2

The argument of an extremal dilatation
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by Marvin Ortel and Wayne Smith PDF

Proc. Amer. Math. Soc. 104 (1988), 498-502 Request permission

Abstract:

Suppose $\kappa$ is the complex dilatation of an extremal quasiconformal homeomorphism of the unit disk onto itself. Then, except in special cases, the width of the set of arguments of $\kappa$ must strictly exceed $\pi$.

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Some properties of conjugate functions

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