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Limit points of lines of minima in Thurston's boundary of Teichmüller space

Díaz Sánchez, Raquel and Series, Caroline (2003) Limit points of lines of minima in Thurston's boundary of Teichmüller space. Algebraic and Geometric Topology, 3 . pp. 207-234. ISSN 1472-2747

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Abstract

Given two measured laminations µ and ν in a hyperbolic sur-face which fill up the surface, Kerckhoff defines an associated line of minima along which convex combinations of the length functions of µ andν are minimised. This is a line in Teichmüller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when µ is uniquely ergodic, this line converges to the projective lamination [µ], but that when µ is rational, the line converges not to [µ], but rather to the barycentre of the support of µ. Similar results on the behaviour of Teichmüller geodesics have been proved by Masur


Item Type:Article
Uncontrolled Keywords:Moduli of Riemann surfaces, Teichmüller theory; Fuchsian groups and their generalizations; Teichmüller theory; Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems; Geometric structures on low-dimensional manifolds
Subjects:Sciences > Mathematics > Geometry
ID Code:15710
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Deposited On:21 Jun 2012 08:59
Last Modified:06 Feb 2014 10:30

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