Geodesics on Riemann Surfaces and their corresponding Limit Points

Artikel i vetenskaplig tidskrift, 2003

The motivation of this paper is twofold. We address the following question, left open by the author in an earlier paper \cite{asf} dealing with a connection of discrete groups and potential theory. Let $\n$ be the set on the unit sphere where a union of hyperbolic spheres centered at each orbitpoint of a discrete group is not minimally thin.{\em Is $\n$ equal to the conical limit set?} We will show that this is not true in general by constructing a counterexample in Section \ref{sec.jg}. The construction utilizes results derived while considering a problem, suggested to the author by Chris Bishop, about generalizing the well known result which gives the correspondence between returning geodesics on Riemann manifolds and conical limit points.