Abstract
The group of one-to-one conformai mappings of the extended plane onto itself is given analytically by the set of linear fractional transformations of the form
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R. Nevanlinna [12].
One says that a Jordan are γ belonging to the boundary Γ is “free” provided none of its interior points is a point of accumulation of boundary points lying exterior to γ.
A. Speiser [2], R. Nevanlinna [10], G. Elfving [1].
Cf. F. Nevanlinna [2].
It the boundary point a ν is the point at infinity, z — a ν in the above expression has to be replaced by 1/z.
Even for this particular choice of the curves q ν , both “halves” of a fundamental region are in general not reflections of one another. One can show that this is the case only when all the points a ν lie on a circle.
Cf. e.g. C. Carathéodory [4].
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© 1970 Springer-Verlag Berlin Heidelberg
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Nevanlinna, R. (1970). Conformal Mapping of Simply and Multiply Connected Regions. In: Eckmann, B., van der Waerden, B.L. (eds) Analytic Functions. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85590-0_2
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DOI: https://doi.org/10.1007/978-3-642-85590-0_2
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