A characterization of short curves of a Teichmueller geodesic

Abstract

We provide a combinatorial condition characterizing curves that are short along a Teichmueller 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 Teichmueller geodesic, and we provide examples demonstrating that the converse is not true.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper5.abs.html

Cited by in corpus (27)

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• Uniform hyperbolicity of the curve graph via surgery sequences
• Length spectra and degeneration of flat metrics
• Hyperbolicity in Teichmüller space
• Covers and the curve complex
• Large scale rank of Teichmuller space
• Invariant Radon measures on measured lamination space
• The shadow of a Thurston geodesic to the curve graph
• On train track splitting sequences
• The augmented marking complex of a surface
• Coarse and fine geometry of the Thurston metric
• Bounded combinatorics and uniform models for hyperbolic 3-manifolds
• Geometry and Rank of Fibered Hyperbolic 3-Manifolds
• Simple closed geodesics and the study of Teichmüller spaces
• Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations
• Random veering triangulations are not geometric
• Volumes of random 3-manifolds
• Relations in Bounded Cohomology
• Small eigenvalues of random 3-manifolds
• Horowitz-Randol pairs of curves in q-differential metrics
• Affine diffeomorphism groups are undistorted
• Logarithmic laws and unique ergodicity
• Hyperbolic spaces in Teichmüller spaces
• Length spectra and strata of flat metrics
• Random walks and contracting elements I: Deviation inequality and Limit laws
• Length of a curve is quasi-convex along a Teichmuller geodesic
• Thick-thin decomposition for quadratic differentials