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# Geodesics on Riemann Surfaces and their corresponding Limit Points

Torbjörn Lundh (Institutionen för matematik)
Michigan Mathematical Journal (0026-2285). Vol. 51 (2003), p. 279-304.

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.

Nyckelord: Discrete group, Fuchsian group, Kleinian group, horocycle, limit set, non-tangential limit set, minimal thinness

CPL Pubid: 23849

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# Institutioner (Chalmers)

Institutionen för matematik (2002-2004)