%0 Journal Article
%A Díaz Sánchez, Raquel
%A Series, Caroline
%T Limit points of lines of minima in Thurston's boundary of Teichmüller space
%D 2003
%@ 1472-2747
%U https://hdl.handle.net/20.500.14352/57389
%X 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
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