On Mostow rigidity for variable negative curvature
  We prove a finiteness theorem for the class of complete finite volume Riemannian manifolds with pinched negative sectional curvature, fixed fundamental group, and of dimension $>2$. One of the key ingredients is that the fundamental group of such a manifold does not admit a small nontrivial action on an $R$-tree. 
Igor Belegradek (McMaster University)