Geodesics on open surfaces containing horns

Maciej Wojtkowski

Displaying similar documents to “Geodesics on open surfaces containing horns”

Geodesic laminations with transverse Hölder distributions

Francis Bonahon (1997)

Annales scientifiques de l'École Normale Supérieure

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Length functions and parameterizations of Teichmüller space for surfaces with cusps.

Hämenstadt, Ursula (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

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Continuity of the bending map

Cyril Lecuire (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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The bending map of a hyperbolic $3$ -manifold maps a convex cocompact hyperbolic metric on a $3$ -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.