Lowest uniformizations of closed Riemann orbifolds
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 639-649 / Harvested from Project Euclid
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.
Publié le : 2010-06-15
Classification:  orbifolds,  Schottky groups,  Kleinian groups,  30F10,  30F40
@article{1275671314,
     author = {Hidalgo
, 
Rub\'en A.},
     title = {Lowest uniformizations of closed Riemann orbifolds},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 639-649},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1275671314}
}
Hidalgo
, 
Rubén A. Lowest uniformizations of closed Riemann orbifolds. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  639-649. http://gdmltest.u-ga.fr/item/1275671314/