Díaz Sánchez, Raquel and Series, Caroline (2003) Limit points of lines of minima in Thurston's boundary of Teichmüller space. Algebraic and Geometric Topology, 3 . pp. 207-234. ISSN 1472-2747
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Given two measured laminations µ and ν in a hyperbolic sur-face which fill up the surface, Kerckhoff defines an associated line of minima along which convex combinations of the length functions of µ andν are minimised. This is a line in Teichmüller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when µ is uniquely ergodic, this line converges to the projective lamination [µ], but that when µ is rational, the line converges not to [µ], but rather to the barycentre of the support of µ. Similar results on the behaviour of Teichmüller geodesics have been proved by Masur
|Uncontrolled Keywords:||Moduli of Riemann surfaces, Teichmüller theory; Fuchsian groups and their generalizations; Teichmüller theory; Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems; Geometric structures on low-dimensional manifolds|
|Subjects:||Sciences > Mathematics > Geometry|
A. J. Casson and S. A. Bleiler. Automorphisms of surfaces after Nielsen and Thurston. LMS Lecture Notes 9. Cambridge University Press, 1988
F. Bonahon. Bouts des variétés de dimension 3. Ann. Math. 124(1), 71–158, 1986.
R. Díaz and C. Series. Examples of pleating varieties for the twice punctured torus. Trans. A.M.S., to appear.
A. Fahti, P. Laudenbach, and V. Poénaru. Travaux de Thurston sur les surfaces, Astérisque 66–67. Société Mathématique de France, 1979.
E. Ghys and P. de la Harpe (eds.). Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math. 83. Birkhäuser, 1990
S. Kerckhoff. Earthquakes are analytic. Comment. Mat. Helv. 60, 17–30, 1985.
S. Kerckhoff. The Nielsen realization problem. Ann. Math. 117(2), 235–265, 1983.
S. Kerckhoff. Lines of Minima in Teichmüller space. Duke Math J. 65, 187–213, 1992.
H. Masur. Two boundaries of Teichmüller space. Duke Math. J. 49, 183–190, 1982.
R. C. Penner with J. Harer. Combinatorics of Train Tracks. Annals of Math. Studies 125. Princeton University Press, 1992.
J-P. Otal. Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3. Astérisque 235. Société Mathématique de France, 1996
1M. Rees. An alternative approach to the ergodic theory of measured foliations on surfaces. Ergodic Th. and Dyn. Sys. 1, 461–488, 1981.
C. Series. An extension of Wolpert's derivative formula. Pacific J. Math. 197, 223–239, 2000.
C. Series. On Kerckhoff Minima and Pleating Loci for Quasifuchsian Groups. Geometriae Dedicata 88, 211–237, 2001.
C. Series. Limits of quasifuchsian groups with small bending. Warwick preprint, July 2002.
W.P. Thurston. The Geometry and Topology of Three-Manifolds. Lecture notes, Princeton University, 1980.
|Deposited On:||21 Jun 2012 10:59|
|Last Modified:||21 Jun 2012 11:04|
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