Global propagation on causal manifolds

The micro-support of sheaves is a tool to describe local propagation results. A natural problem is then to give sufficient conditions to get global propagation results from the knowledge of the micro-support. This is the aim of this paper. As an application, we consider the problem of global existence for solutions to hyperbolic systems (in the hyperfunction and distribution case), along the lines of Leray. Causal manifolds, and in particular homogeneous causal manifolds as considered by Faraut et al., give examples of manifolds to which our results apply.