Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Lines of minima with no end in Thurston’s boundary of Teichmüller space
HTML articles powered by AMS MathViewer

by Yuki Iguchi PDF
Conform. Geom. Dyn. 16 (2012), 22-43 Request permission


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.
Similar Articles
Additional 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