Uniformization of conformal involutions of stable Riemann Surfaces

Raquel Diaz, jeudi 12 février 2009, 11h15, MA 12

Abstract:

Given a stable Riemann surface $S$  (i.e., a Riemann surface with nodes) 

and a conformal involution $\tau$ on it, we wonder whether there exists 

a Schottky uniformization of the stable Riemann surface such that $\tau$ 

lifts to this uniformization. From the 3-dimensional hyperbolic point of 

view this means that, given $S$ and $\tau$, we are looking for a 

hyperbolic structure on a handlebody, whose conformal boundary at 

infinity is $S$ and such that $\tau$ extends to an isometry of this 

hyperbolic structure.

We give partial solutions for this problem.