On moduli of plane domains
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- by Ignacio Guerrero PDF
- Proc. Amer. Math. Soc. 67 (1977), 41-49 Request permission
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 $\Omega$ be a plane domain bounded by $m \geqslant 3$ continua. Denote by $T(\Omega )$ the reduced Teichmüller space of $\Omega$ and by $R(\Omega )$ the space of conformal equivalence classes of domains bounded, as $\Omega$ is, by m continua. A real analytic map from $T(\Omega )$ onto an open subset $S(\Omega )$ of a $3m - 6$ dimensional product of circles and lines is constructed. It is shown that the map $T(\Omega ) \to S(\Omega )$ is a regular covering map. Finally, it is observed that there is a finite sheeted covering map $S(\Omega ) \to R(\Omega )$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- 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