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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $S(\Omega ) \to R(\Omega )$.
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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