Lowest uniformizations of compact Klein surfaces

  • Rubén A. Hidalgo

    Universidad Técnica Federico Santa María, Valparaíso, Chile


A Schottky group is a purely loxodromic Kleinian group, with a nonempty region of discontinuity, isomorphic to a free group of finite rank. An extended Schottky group is an extended Kleinian group whose orientation-preserving half is a Schottky group. The collection of uniformizations of either a closed Riemann surface or a compact Klein surface is partially ordered. In the case of closed Riemann surfaces, the lowest uniformizations are provided by Schottky groups. In this paper we provide simple arguments to see that the lowest uniformizations of compact Klein surfaces are exactly those produced by extended Schottky groups.

Cite this article

Rubén A. Hidalgo, Lowest uniformizations of compact Klein surfaces. Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 373–379

DOI 10.4171/RMI/724