Abstract:In this paper, we consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem by the author in On behavior of pairs of Teichmüller geodesic rays, 2014 . We also consider the infimum of the asymptotic distance up to choice of base points of the rays along the geodesics. We show that the infimum is represented by two quantities. One is the detour metric between the end points of the rays on the Gardiner-Masur boundary of the Teichmüller space, and the other is the Teichmüller distance between the end points of the rays on the augmented Teichmüller space.
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- Masanori Amano
- Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguroku, Tokyo 152-8551, Japan
- Email: firstname.lastname@example.org
- Received by editor(s): February 14, 2014
- Received by editor(s) in revised form: May 14, 2014
- Published electronically: September 5, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Conform. Geom. Dyn. 18 (2014), 157-170
- MSC (2010): Primary 32G15; Secondary 30F60
- DOI: https://doi.org/10.1090/S1088-4173-2014-00268-9
- MathSciNet review: 3255426