Gluing variations

Abstract

We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions d ≥ 4, with emphasis on characteristic data. A useful tool is provided by the notion of submanifold-data of order k. As an application of our methods we prove that vacuum Cauchy data on a spacelike Cauchy surface with boundary can always be extended to vacuum data defined beyond the boundary.