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abstract: 'We study geodesics on planar Riemann surfaces 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.'
author:
- Andrew Haas and Perry Susskind
title: The geometry at infinity of a hyperbolic Riemann surface of infinite type 
---

introduction
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A flute surface $S$ is most simply described as a connected domain in the complex plane, for which all but one of the components in the complement of $S$ is isolated from the others. Flute surfaces were first considered by Basmajian [@bas1] as examples of the simplest sort of hyperbolic Riemann surface of infinite type. A flute surface has a single infinite end. The presence of such an infinite end, even one of this simple sort, allows for many different possibilities for the geometry of the surface, which have no parallels in the theory of finite surfaces. In this paper, our main concern is with the behavior of the geometry associated to the infinite end 