Open Access
June, 2010 Lowest uniformizations of closed Riemann orbifolds
Rubén A. Hidalgo
Rev. Mat. Iberoamericana 26(2): 639-649 (June, 2010).


A Kleinian group containing a Schottky group as a finite index subgroup is called a Schottky extension group. If $\Omega$ is the region of discontinuity of a Schottky extension group $K$, then the quotient $\Omega/K$ is a closed Riemann orbifold; called a Schottky orbifold. Closed Riemann surfaces are examples of Schottky orbifolds as a consequence of the Retrosection Theorem. Necessary and sufficient conditions for a Riemann orbifold to be a Schottky orbifold are due to M. Reni and B. Zimmermann in terms of the signature of the orbifold. It is well known that the lowest uniformizations of a closed Riemann surface are exactly those for which the Deck group is a Schottky group. In this paper we extend such a result to the class of Schottky orbifolds, that is, we prove that the lowest uniformizations of a Schottky orbifold are exactly those for which the Deck group is a Schottky extension group.


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Rubén A. Hidalgo . "Lowest uniformizations of closed Riemann orbifolds." Rev. Mat. Iberoamericana 26 (2) 639 - 649, June, 2010.


Published: June, 2010
First available in Project Euclid: 4 June 2010

zbMATH: 1214.30028
MathSciNet: MR2677010

Primary: 30F10 , 30F40

Keywords: Kleinian groups , orbifolds , Schottky groups

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.26 • No. 2 • June, 2010
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