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Dirichlet points, Garnett points, and infinite ends of hyperbolic surfaces. I. (English) Zbl 0846.30028
Summary: The end of a hyperbolic surface is studied in terms of the behavior at infinity of geodesics on the surface. For a class of surfaces called untwisted flutes it is possible to give a fairly precise description of the ending geometry. From the point of view of a Fuchsian group representing such a surface this provides new information about the existence of Dirichlet and Garnett points.

30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
53C22 Geodesics in global differential geometry
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