# zbMATH — the first resource for mathematics

A characterization of short curves of a Teichmüller geodesic. (English) Zbl 1082.30037
In this paper, the author obtains a combinatorial condition to characterize short curves along a Teichmüller geodesic. This condition is similar to the one given by Minsky for a hyperbolic 3-manifold. He shows that short curves in a hyperbolic manifold homeomorphic to $$S\times R$$ are also short in the corresponding Teichmüller geodesic, and he provides examples demonstrating that its converse is false.

##### MSC:
 30F60 Teichmüller theory for Riemann surfaces 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
##### Keywords:
Teichmüller geodesic; short curve
Full Text:
##### References:
 [1] J Brock, D Canary, Y Minsky, The classification of Kleinian surface groups II: the ending lamination conjecture, in preparation · Zbl 1253.57009 · doi:10.4007/annals.2012.176.1.1 [2] Y Minsky, The classification of Kleinian surface groups I: models and bounds · Zbl 1193.30063 · doi:10.4007/annals.2010.171.1 · annals.princeton.edu [3] K Rafi, Hyperbolic 3-manifolds and geodesics in Teichmüller space, PhD thesis, SUNY at Stony Brook (2001) [4] M Rees, The geometric model and large Lipschitz equivalence direct from Teichmüller geodesic, preprint · www.liv.ac.uk
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.