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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## Abstract

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

Item Type: | Article |
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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 |

ID Code: | 15710 |

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Deposited On: | 21 Jun 2012 08:59 |

Last Modified: | 06 Feb 2014 10:30 |

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