Notation. The main objects of this paper are n-tuples y = (y1, . . . , yn) of real numbers viewed as linear forms, i.e. as row vectors. In what follows, y will always mean a row vector, and we willâ€¦ (More)

The main objective of this paper is to prove a Khintchine type theorem on divergence of linear Diophantine approximation on nondegenerate manifolds, which completes earlier results for convergence.â€¦ (More)

Let Î“ be a discrete group with property (T) of Kazh-dan. We prove that any Riemannian isometric action of Î“ on a compact manifold X is locally rigid. We also prove a more general foliated version ofâ€¦ (More)

Let Î“0 âŠ‚ O(2, 1) be a Schottky group, and let Î£ = H2/Î“0 be the corresponding hyperbolic surface. Let C(Î£) denote the space of geodesic currents on Î£. The cohomology group H1(Î“0, V) parametrizesâ€¦ (More)

We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniformâ€¦ (More)

For n > 1, a generic nâ€“tuple of elements in a connected compact non-abelian Lie group G generates a free group. G.A. Margulis and G.A. Soifer [11] conjectured that every such tuple can be slightlyâ€¦ (More)