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

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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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Official URL: http://emis.math.ca/journals/UW/agt/ftp/main/2003/agt-3-9.pdf


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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
Deposited On:21 Jun 2012 08:59
Last Modified:18 Feb 2019 12:39

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