Uniformization of conformal involutions on stable Riemann surfaces

作者：Diaz Raquel^*; Garijo Ignacio; Hidalgo Ruben A

来源：Israel Journal of Mathematics, 2011, 186(1): 297-331.

DOI：10.1007/s11856-011-0141-2

Let S be a closed Riemann surface of genus g. It is well known that there are Schottky groups producing uniformizations of S (Retrosection Theorem). Moreover, if tau: S -> S is a conformal involution, it is also known that there is a Kleinian group K containing, as an index two subgroup, a Schottky group G that uniformizes S and so that K/G induces the cyclic group aOE (c)tau >. Let us now assume S is a stable Riemann surface and tau: S -> S is a conformal involution. Again, it is known that S can be uniformized by a suitable noded Schottky group, but it is not known whether or not there is a Kleinian group K, containing a noded Schottky group G of index two, so that G uniformizes S and K/G induces aOE (c)tau >. In this paper we discuss this existence problem and provide some partial answers: (1) a complete positive answer for genus g a parts per thousand currency sign 2 and for the case that S/aOE (c)tau > is of genus ze

• 出版日期2011-11