Contact process in a wedge

We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor ``grass-bushes-trees'' successional model introduced in Durrett and Swindle (1991).