A characterization of short curves of a Teichmuller geodesic

被引:63
作者
Rafi, K [1 ]
机构
[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
关键词
Teichmuller space; geodesic; short curves; complex of curves; Kleinian group; bounded geometry;
D O I
10.2140/gt.2005.9.179
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We provide a combinatorial condition characterizing curves that are short along a Teichmuller geodesic. This condition is closely related to the condition provided by Minsky for curves in a hyperbolic 3-manifold to be short. We show that short curves in a hyperbolic manifold homeomorphic to S x R are also short in the corresponding Teichmuller geodesic, and we provide examples demonstrating that the converse is not true.
引用
收藏
页码:179 / 202
页数:24
相关论文
共 18 条
[1]  
[Anonymous], 2000, MATH SURVEYS MONOGR
[2]  
Bers L., 1960, Bull. Amer. Math. Soc, V66, P94, DOI [10.1090/S0002-9904-1960-10413-2, DOI 10.1090/S0002-9904-1960-10413-2]
[3]   ENDS OF HYPERBOLIC MANIFOLDS OF DIMENSION-3 [J].
BONAHON, F .
ANNALS OF MATHEMATICS, 1986, 124 (01) :71-158
[4]  
BROCK JF, UNPUB CLASSIFICATION, V2
[5]  
GARDINER FP, 2000, COMPLEX VARIABLES TH, V16, P209
[6]   COMPARISON OF HYPERBOLIC AND EXTREMAL LENGTHS [J].
MASKIT, B .
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1985, 10 (01) :381-386
[7]   Geometry of the complex of curves I: Hyperbolicity [J].
Masur, HA ;
Minsky, YN .
INVENTIONES MATHEMATICAE, 1999, 138 (01) :103-149
[8]   Geometry of the complex of curves II: Hierarchical structure [J].
Masur, HA ;
Minsky, YN .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2000, 10 (04) :902-974
[9]  
MINSKY Y, MATHGT0302208
[10]   Kleinian groups and the complex of curves [J].
Minsky, Yair N. .
GEOMETRY & TOPOLOGY, 2000, 4 :117-148