  Given a truncated incoming null cone and a truncated outgoing null cone
intersecting at a two sphere $S$ with smooth characteristic initial data, a
theorem of Rendall shows that the vacuum Einstein equations can be solved in a
small neighborhood of $S$ in the future of $S$. We show that in fact the vacuum
Einstein equations can be solved in a neighborhood in the future of the cones,
as long as the constraint equations are initially satisfied on the null cones.
The proof is based on energy type estimates and relies heavily on the null
structure of the Einstein equations in the double null foliation.
