Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S is a closed Klein surface, then κ can also be lifted to a suitable extended-Schottky uniformization.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-2-4,
author = {Rub\'en A. Hidalgo},
title = {Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {161-180},
zbl = {1238.30028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-2-4}
}
Rubén A. Hidalgo. Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations. Fundamenta Mathematicae, Tome 215 (2011) pp. 161-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-2-4/