Remote Access Conformal Geometry and Dynamics
Green Open Access

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
MathSciNet review: 2890254
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30F45, 30F60, 32G15, 57M15, 57M50, 32G15, 30F60, 30F45

Retrieve articles in all journals with MSC (2010): 30F45, 30F60, 32G15, 57M15, 57M50, 32G15, 30F60, 30F45

Additional Information

Yuki Iguchi
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

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.