A remark on angular complex dilatations of quasiconformal mappings
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- by Richard Fehlmann PDF
- Proc. Amer. Math. Soc. 104 (1988), 1071-1077 Request permission
Abstract:
By a theorem of Ortel an angular complex dilatation $\kappa$ is extremal iff it is Teichmüllèr (quadratic differential with finite norm) or if it satisfies an integral condition involving the angular limits ${\lambda _x}(\vartheta )$. We show that this second case occurs iff ${\lambda _x}(\vartheta )$ can be given explicitly at a certain point $x$, namely by ${\lambda _x}(\vartheta ) = {\left \| \kappa \right \|_\infty }{e^{2i}}(\vartheta - {\vartheta _0})$. Moreover, we investigate this statement under the weaker condition of angularity when the uniformity part in its definition is dropped.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1071-1077
- MSC: Primary 30C60; Secondary 30C75
- DOI: https://doi.org/10.1090/S0002-9939-1988-0930251-3
- MathSciNet review: 930251