Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 381-408
University of Aarhus, Department of Mathematical Sciences
Ny Munkegade, Building 1530, DK-8000 Aarhus C, Denmark;
theret 'at' imf.au.dk
Abstract. Stretch lines are geodesics for Thurston's asymmetric metric on Teichmüller space [10]. Each stretch line is directed by a complete geodesic lamination. An anti-stretch line directed by the complete geodesic lamination \mu is a stretch line directed by \mu traversed in the opposite direction. It is not necessarily a geodesic. In this paper, we tackle the problem of the convergence (or non-convergence) of anti-stretch lines towards a point of Thurston's boundary of Teichmüller space. We show that an anti-stretch line directed by a complete geodesic lamination \mu which is made up of a compact and uniquely ergodic measured sublamination \gamma, with its other leaves spiraling around it, converges to the projective class of \gamma.
2000 Mathematics Subject Classification: Primary 30F60, 57M50, 53C22.
Key words: Teichmüller space, hyperbolic structure, geodesic lamination, stretch, Thurston's boundary, measured foliation.
Reference to this article: G. Théret: On the negative convergence of Thurston's stretch lines. Ann. Acad. Sci. Fenn. Math. 32 (2007), 381-408.
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