The shadow of a Thurston geodesic to the curve graph
  We study the geometry of the Thurston metric on Teichmuller space by examining its geodesics and comparing them to Teichmuller geodesics. We show that, similar to a Teichmuller geodesic, the shadow of a Thurston geodesic to the curve graph is a reparametrized quasi-geodesic. However, we show that the set of short curves along the two geodesics are not identical. 
Anna Lenzhen, Kasra Rafi and Jing Tao
math.GT