Mostow rigidity and the marked length spectrum

Collection Mostow rigidity and the marked length spectrum

We give an outline of Sullivan's proof of Mostow rigidity theorem for closed hyperbolic manifolds, using the notions of Patterson-Sullivan measures for discrete groups acting on CAT(-1) spaces, and the Bowen-Margulis measure, or the measure of maximal entropy for the geodesic flow of a closed negatively curved manifold. We also describe how these ideas lead to an equivalence between the following objects for a closed manifold of variable negative curvature: the marked length spectrum, the geodesic flow, and the cross-ratio on the boundary of the universal cover.


Organizer(s) Arindam Bhattacharyya, Peter Haissinsky
linked URL http://phaissin.perso.math.cnrs.fr/CIMPAKolkata/indexcimpa-kolkata.html
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