Geometriae Dedicata

, Volume 173, Issue 1, pp 393–415 | Cite as

Refined gluing for vacuum Einstein constraint equations

Original Paper
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Abstract

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 every 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.

Keywords

Einstein constraint equations Conformal method Connected sum 

Mathematics Subject Classification (2000)

53C21 58J60 83C05 
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Notes

Acknowledgments

The first author is partially supported by the french project ANR-10-BLAN 0105 ACG and the ANR SIMI-1-003-01 GR-A-G. The second author is supported by the Italian project FIRB–IDEAS ‘Analysis and Beyond’ and he is grateful to the University of Avignon for the hospitality during the preparation of this work.

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Copyright information

© European Union 2014

Authors and Affiliations

  1. 1.Faculté des SciencesLaboratoire de mathématiques d’AvignonAvignonFrance
  2. 2.Scuola Normale SuperiorePisaItaly

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