We characterize which cobounded quasigeodesics in the Teichmüller space of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path in , we show that is a quasigeodesic with finite Hausdorff distance from some geodesic if and only if the canonical hyperbolic plane bundle over is a hyperbolic metric space. As an application, for complete hyperbolic 3–manifolds with finitely generated, freely indecomposable fundamental group and with bounded geometry, we give a new construction of model geometries for the geometrically infinite ends of , a key step in Minsky’s proof of Thurston’s ending lamination conjecture for such manifolds.
"Stable Teichmüller quasigeodesics and ending laminations." Geom. Topol. 7 (1) 33 - 90, 2003. https://doi.org/10.2140/gt.2003.7.33