The type problem for Riemann surfaces via Fenchel-Nielsen parameters

Ara Basmajian, Hrant Hakobyan, Dragomir Šarić

A Riemann surface $X$ is said to be of \emph{parabolic type} if it supports a Green's function. Equivalently, the geodesic flow on the unit tangent of $X$ is ergodic. Given a Riema…