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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Lines of minima with no end in Thurston's boundary of Teichmüller space


Author: Yuki Iguchi
Journal: Conform. Geom. Dyn. 16 (2012), 22-43
MSC (2010): Primary 30F45, 30F60, 32G15, 57M15; Secondary 57M50, 32G15, 30F60, 30F45
Published electronically: March 7, 2012
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Abstract: Let $ \nu ^+$ and $ \nu ^-$ be two measured laminations which fill up a hyperbolic surface. Kerckhoff [Duke Math. J. 65 (1992), 187-213] defines a line of minima as a family of surfaces where convex combinations of the hyperbolic length functions of $ \nu ^+$ and $ \nu ^-$ are minimum. This is a proper curve in the Teichmüller space. We show that there exists a line of minima which does not converge in the Thurston compactification of the Teichmüller space of a compact Riemann surface. We also show that the limit set of the line of minima is contained in a simplex on the Thurston boundary.


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Additional Information

Yuki Iguchi
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
Email: iguchi.y.ac@m.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S1088-4173-2012-00240-8
PII: S 1088-4173(2012)00240-8
Keywords: Teichmüller space, Thurston’s boundary, Teichmüller geodesic, line of minima.
Received by editor(s): August 2, 2011
Published electronically: March 7, 2012
Additional Notes: The author is partially supported by “Global COE: Computationism as a Foundation for the Sciences”.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.