2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163809We study geodesics on a planar Riemann surface of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these geodesics and relate them to the structure of the boundary of a Dirichlet polygon for a Fuchsian group representing the surface.32 pagesGeometric TopologyComplex Variables30F35; 30F45The geometry at infinity of a hyperbolic Riemann surface of infinite typetext