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Stable Teichmüller quasigeodesics and ending laminations. (English) Zbl 1021.57009
The authors abstract: ”We characterize which cobounded quasigeodesics in the Teichmüller space $${\mathcal T}$$ of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded Lipschitz path $$\gamma$$ in $${\mathcal T}$$, we show that $$\gamma$$ is a quasigeodesic with finite Hausdorff distance from some geodesic if and only if the canonical hyperbolic plane bundle over $$\gamma$$ is a hyperbolic metric space. As an application, for complete hyperbolic 3-manifolds $$N$$ 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 $$N$$, a key step in Minsky’s proof of Thurston’s ending lamination conjecture for such manifolds [J. Am. Math. Soc. 7, No. 3, 539-588 (1994; Zbl 0808.30027)].

##### MSC:
 57M50 General geometric structures on low-dimensional manifolds 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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