Linearization and mappings onto pseudocircle domains
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- Trans. Amer. Math. Soc. 282 (1984), 415-429 Request permission
Abstract:
We demonstrate the existence of linearizations for groups of conformal and anticonformal homeomorphisms of Riemann surfaces. The finitely generated groups acting on plane domains are classified in terms of specific linearizations. This extends Maskit’s work in the directly conformal case. As an application we prove that there exist conformal representations of finite genus open Riemann surfaces for which accessible boundary points are either isolated or lie on circular arcs of pseudocircular boundary components. In many cases these are actually circle domains. Along the way we extend the applicability of Carathéodory’s boundary correspondence theorem for prime ends.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 415-429
- MSC: Primary 30F40; Secondary 30D40
- DOI: https://doi.org/10.1090/S0002-9947-1984-0728721-7
- MathSciNet review: 728721