On moduli of plane domains

Author:
Ignacio Guerrero

Journal:
Proc. Amer. Math. Soc. **67** (1977), 41-49

MSC:
Primary 32G15; Secondary 30A46

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454074-X

MathSciNet review:
0454074

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Abstract: It is well known that an arbitrary plane domain of finite connectivity can be mapped conformally onto an annulus minus a certain number of circular slits. The parameters defining such a canonical domain are studied in the context of Teichmüller theory.

Let be a plane domain bounded by continua. Denote by the reduced Teichmüller space of and by the space of conformal equivalence classes of domains bounded, as is, by *m* continua. A real analytic map from onto an open subset of a dimensional product of circles and lines is constructed. It is shown that the map is a regular covering map. Finally, it is observed that there is a finite sheeted covering map .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454074-X

Keywords:
Plane domain,
moduli,
Teichmüller space

Article copyright:
© Copyright 1977
American Mathematical Society