The geodesic flow on infinite type hyperbolic surfaces

Ara Basmajian (CUNY)

Abstract: As part of an ongoing project we describe results involving the relationship between Fenchel-Nielsen coordinates and a version of the classical type problem (whether or not the Riemann surface carries a Green's function) on infinite type surfaces. Since non-existence of a Green's function is equivalent to ergodicity of the geodesic flow we provide geometric criteria on any infinite type surface to guarantee such behavior. This is joint work with Hrant Hakobyan and Dragomir Saric.