We prove that the embedding of the Teichm\"uller space in the space of geodesic currents is totally linearly independent. As a corollary we get a rigidity result for the marked length spectrum of anti-de Sitter quasi-Fuchsian manifolds.

Let $S$ be a closed surface of genus $g \geq 2$ and let $\rho$ be a maximal $\mathrm{PSL}(2, \mathbb{R}) \times \mathrm{PSL}(2, \mathbb{R})$ surface group representation. By a result of Schoen, there… Expand

This paper is unpublished work of Geoffrey Mess written in 1990, which gives a classification of flat and anti-de Sitter domains of dependence in 2+1 dimensions.

Abstract. Let G be a reductive linear real Lie group and
$\Gamma$ be a Zariski dense subgroup. We study asymptotic properties of
$\Gamma$ through the set of logarithms of the radial components of… Expand

We propose a definition for the length of closed geodesics in a globally hyperbolic maximal compact (GHMC) Anti-De Sitter manifold. We then prove that the number of closed geodesics of length less… Expand

Let Gamma be a cocompact lattice in SO(1,n). A representation rho: Gamma \to SO(2,n) is quasi-Fuchsian if it is faithfull, discrete, and preserves an acausal subset in the boundary of anti-de Sitter… Expand