Abstract
Given two measured laminations and in a hyperbolic surface which fill up the surface, Kerckhoff [Lines of Minima in Teichmueller space, Duke Math J. 65 (1992) 187–213] defines an associated line of minima along which convex combinations of the length functions of and 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 is uniquely ergodic, this line converges to the projective lamination , but that when is rational, the line converges not to , but rather to the barycentre of the support of . Similar results on the behaviour of Teichmüller geodesics have been proved by Masur [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183–190].
Citation
Raquel Diaz. Caroline Series. "Limit points of lines of minima in Thurston's boundary of Teichmüller space." Algebr. Geom. Topol. 3 (1) 207 - 234, 2003. https://doi.org/10.2140/agt.2003.3.207
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