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We characterize which cobounded quasigeodesics in the Teichmueller space T ofa closed surface are at bounded distance from a geodesic. More generally, givena cobounded lipschitz path gamma in T, we show that gamma is a quasigeodesicwith finite Hausdorff distance from some geodesic if and only if the canonicalhyperbolic plane bundle over gamma is a hyperbolic metric space. As anapplication, for complete hyperbolic 3-manifolds N with finitely generated,freely indecomposable fundamental group and with bounded geometry, we give anew construction of model geometries for the geometrically infinite ends of N,a key step in Minsky's proof of Thurston's ending lamination conjecture forsuch manifolds.

Stable Teichmüller quasigeodesics and ending laminations