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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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Lines of minima with no end in Thurston’s boundary of Teichmüller space
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by Yuki Iguchi
Conform. Geom. Dyn. 16 (2012), 22-43
Published electronically: March 7, 2012


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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Bibliographic Information
  • Yuki Iguchi
  • Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
  • Email:
  • 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”.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 16 (2012), 22-43
  • MSC (2010): Primary 30F45, 30F60, 32G15, 57M15; Secondary 57M50, 32G15, 30F60, 30F45
  • DOI:
  • MathSciNet review: 2890254