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

MathSciNet review:
2890254

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and 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 and 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:
https://doi.org/10.1090/S1088-4173-2012-00240-8

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.