### A characterization of short curves of a Teichmüller geodesic.

Rafi, Kasra (2005)

Geometry & Topology

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Rafi, Kasra (2005)

Geometry & Topology

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Minsky, Yair N. (2000)

Geometry & Topology

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Hämenstadt, Ursula (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

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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.

Luo, Feng, Stong, Richard (2002)

Geometry & Topology

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Mark Comerford (2011)

Open Mathematics

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We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We...

Parlier, Hugo (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

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Francis Bonahon (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Lackenby, Marc (2002)

Geometry & Topology

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Neumann-Coto, Max (2001)

Algebraic & Geometric Topology

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