3/10/2005

Sa'ar-David Hersonsky
Princeton University

Diophantine approximations on negatively curved manifolds

Inspired by the theory of Diophantine approximation of a real (or complex) number by rational ones, we develop a theory of approximation of geodesic lines in a negatively curved Riemannian manifold. The talk will be a survey on some of our results: We prove a Dirichlet type theorem, define a Hurwitz type constant in terms of the lengths of closed geodesics, and a Khintchine-Sullivan type theorem on the Hausdorff measure of the geodesic lines starting from a cusp that are well approximated by cusp returning ones. This is a joint project with Frederic Paulin (ENS-Paris).