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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

The asymptotic behavior of Jenkins-Strebel rays


Author: Masanori Amano
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
Published electronically: September 5, 2014
MathSciNet review: 3255426
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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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Additional Information

Masanori Amano
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguroku, Tokyo 152-8551, Japan
Email: amano.m.ab@m.titech.ac.jp

DOI: https://doi.org/10.1090/S1088-4173-2014-00268-9
Keywords: Teichm\"uller space, Teichm\"uller distance, Teichm\"uller geodesic, augmented Teichm\"uller space
Received by editor(s): February 14, 2014
Received by editor(s) in revised form: May 14, 2014
Published electronically: September 5, 2014
Article copyright: © Copyright 2014 American Mathematical Society