Given two measured laminations μ and ν in a hyperbolic surface which fill up the surface, Kerckhoff [Lines of Minima in Teichmueller space, Duke Math J. 65 (1992) 187–213] defines an associated line of minima along which convex combinations of the length functions of μ and ν 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 [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183–190].
Diaz, Raquel 1 ; Series, Caroline 2
@article{10_2140_agt_2003_3_207,
author = {Diaz, Raquel and Series, Caroline},
title = {Limit points of lines of minima in {Thurston{\textquoteright}s} boundary of {Teichm\"uller} space},
journal = {Algebraic and Geometric Topology},
pages = {207--234},
year = {2003},
volume = {3},
number = {1},
doi = {10.2140/agt.2003.3.207},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.207/}
}
TY - JOUR AU - Diaz, Raquel AU - Series, Caroline TI - Limit points of lines of minima in Thurston’s boundary of Teichmüller space JO - Algebraic and Geometric Topology PY - 2003 SP - 207 EP - 234 VL - 3 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.207/ DO - 10.2140/agt.2003.3.207 ID - 10_2140_agt_2003_3_207 ER -
%0 Journal Article %A Diaz, Raquel %A Series, Caroline %T Limit points of lines of minima in Thurston’s boundary of Teichmüller space %J Algebraic and Geometric Topology %D 2003 %P 207-234 %V 3 %N 1 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2003.3.207/ %R 10.2140/agt.2003.3.207 %F 10_2140_agt_2003_3_207
Diaz, Raquel; Series, Caroline. Limit points of lines of minima in Thurston’s boundary of Teichmüller space. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 207-234. doi: 10.2140/agt.2003.3.207
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