Algebraic and Geometric Topology 3 (2003), paper no. 9, pages 207-234.

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

Raquel Diaz and Caroline Series

Abstract. Given two measured laminations mu and nu 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 mu and nu are minimised. This is a line in Teichmueller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when mu is uniquely ergodic, this line converges to the projective lamination [mu], but that when mu is rational, the line converges not to [mu], but rather to the barycenter of the support of mu. Similar results on the behaviour of Teichmueller geodesics have been proved by Masur [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183-190].

Keywords. Teichmueller space, Thurston boundary, measured geodesic lamination, Kerckhoff line of minima

AMS subject classification. Primary: 20H10. Secondary: 32G15.

DOI: 10.2140/agt.2003.3.207

E-print: arXiv:math.GT/0303108

Submitted: 17 January 2003. Accepted: 3 February 2003. Published: 26 February 2003.

Notes on file formats

Raquel Diaz
Deparmento Geometria y Topologia, Fac. CC. Matematicas
Universidad Complutense, 28040 Madrid, Spain
Caroline series
Mathematics Institute, University of Warwick
Coventry CV4 7AL, UK


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