The type problem for Riemann surfaces via Fenchel–Nielsen parameters
The type problem for Riemann surfaces via Fenchel–Nielsen parameters
A Riemann surface X $X$ is said to be of parabolic type if it does not support a Green's function. Equivalently, the geodesic flow on the unit tangent bundle of X $X$ (equipped with the hyperbolic metric) is ergodic. Given a Riemann surface X $X$ of arbitrary topological type and …