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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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
|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|
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|Deposited On:||21 Jun 2012 10:59|
|Last Modified:||21 Jun 2012 11:04|