Some Lipschitz maps between hyperbolic surfaces with applications to Teichmüller theory
On the Teichmüller space of a hyperbolic surface of finite type, Thurston has introduced an asymmetric metric and studied a class of geodesics for this metric called stretch lines. In the paper under review the authors construct some special stretch lines that are also geodesic lines (up to reparametrization) for Thurston's asymmetric metric when traversed in the reverse direction. These lines are directed by complete geodesic laminations that are not chain-recurrent and have a nice description in terms of the Fenchel-Nielsen coordinates.
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