Abstract
Let be a discrete group. For a pair of representations of into with geometrically finite, we study the set of –equivariant Lipschitz maps from the real hyperbolic space to itself that have minimal Lipschitz constant. Our main result is the existence of a geodesic lamination that is “maximally stretched” by all such maps when the minimal constant is at least . As an application, we generalize two-dimensional results and constructions of Thurston and extend his asymmetric metric on Teichmüller space to a geometrically finite setting and to higher dimension. Another application is to actions of discrete subgroups of on by right and left multiplication: we give a double properness criterion for such actions, and prove that for a large class of groups the action remains properly discontinuous after any small deformation of inside .
Citation
François Guéritaud. Fanny Kassel. "Maximally stretched laminations on geometrically finite hyperbolic manifolds." Geom. Topol. 21 (2) 693 - 840, 2017. https://doi.org/10.2140/gt.2017.21.693
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