Lowest uniformizations of closed Riemann orbifolds (Q986621)

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 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, the author extends such a result to the class of Schottky orbifolds, that is, he proves that the lowest uniformizations of a Schottky orbifold are exactly those for which the Deck group is a Schottky extension group.