Gluing variations

Abstract

We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions $d\ge 4$, 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.

arXiv commentProof for extending vacuum metric on truncated cone extended; typos corrected; now, 30 pages main text + 7 pages appendix, 8 figures

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• Characteristic Gluing with $\Lambda$: III. High-differentiability nonlinear gluing