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2003 Limit points of lines of minima in Thurston's boundary of Teichmüller space
Raquel Diaz, Caroline Series
Algebr. Geom. Topol. 3(1): 207-234 (2003). DOI: 10.2140/agt.2003.3.207


Given two measured laminations μ and ν 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 μ and ν 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 [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183–190].


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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.


Received: 17 January 2003; Accepted: 3 February 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1066.32020
MathSciNet: MR1997320
Digital Object Identifier: 10.2140/agt.2003.3.207

Primary: 20H10
Secondary: 32G15

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.3 • No. 1 • 2003
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