Asymptotic behavior of grafting rays

摘要

In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmüller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmüller geodesics and lines of minima. We also show that the rays grafted along a weighted system of simple closed curves are at bounded distance from Teichmüller geodesics.