Refined gluing for Vacuum Einstein constraint equations

Details Refined gluing for Vacuum Einstein constraint equations Refined gluing for Vacuum Einstein constraint equations

2010-03-22

arxiv.org/abs/1003.4178v1

Mathematics

Differential Geometry

Scientific paper

We first show that the connected sum along submanifolds introduced by the second author for compact initial data sets of the vacuum Einstein system can be adapted to the asymptotically Euclidean and to the asymptotically hyperbolic context. Then, we prove that in any case, and generically, the gluing procedure can be localized, in order to obtain new solutions which coincide with the original ones outside of a neighborhood of the gluing locus.

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