# Métriques de Carnot-Carthéodory et quasiisométries des espaces symétriques de rang un

### Abstract

We exhibit a rigidity property of the simple groups $\mathrm{Sp}(n, 1)$ and $F_4^{-20}$ which implies Mostow rigidity. This property does not extend to $\mathrm{O}(n, 1)$ and $\mathrm{U}(n, 1)$. The proof relies on quasiconformal theory applied in the CR setting. Extensions are given to a class of solvable Lie groups. As a byproduct, a result on quasiisometries of infinite nilpotent groups is obtained.

Pierre Pansu