On the ergodicity of partially hyperbolic group actions

In 1996, Pugh and Shub conjectured that stable ergodicity is Ck-open and dense in the space of Ck, volume-preserving, partially hyperbolic diffeomorphisms. The purpose of this paper is to take the latest results on this conjecture and reformulate them for the more general setting of partially hyperbolic flows or Lie group actions (as opposed to diffeomorphisms). In particular, we will prove that stable ergodicity is Ck-open and dense in the space of Ck, volume-preserving, partially hyperbolic flows with one-dimensional center.