Lines of minima with no end in Thurston's boundary of Teichmüller space
Author:
Yuki Iguchi
Journal:
Conform. Geom. Dyn. 16 (2012), 2243
MSC (2010):
Primary 30F45, 30F60, 32G15, 57M15; Secondary 57M50, 32G15, 30F60, 30F45
Published electronically:
March 7, 2012
MathSciNet review:
2890254
Fulltext PDF Free Access
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Abstract: Let and be two measured laminations which fill up a hyperbolic surface. Kerckhoff [Duke Math. J. 65 (1992), 187213] 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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 K. Strebel, Quadratic Differentials, Springer Verlag, Berlin and New York (1984). MR 743423 (86a:30072)
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 S. Wolpert, The length spectra as moduli for compact Riemann surfaces. Ann. Math. 109 (1979), 323351. MR 528966 (80j:58067)
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Additional Information
Yuki Iguchi
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguroku, Tokyo 1528551, Japan
Email:
iguchi.y.ac@m.titech.ac.jp
DOI:
http://dx.doi.org/10.1090/S108841732012002408
PII:
S 10884173(2012)002408
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.
