On Thurston's Stretch Lines in Teichmüller Space

Abstract

The Teichmüller space $\mathcal{T}(\Sigma )$ of a surface $\Sigma$ is equipped with Thurston's asymmetric metric. Stretch lines are oriented geodesics for this metric on $\mathcal{T}(\Sigma )$. We give the asymptotic behavior of the lengths of the measured geodesic laminations as one follows a stretch line in the positive direction.