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Stability of the Einstein–Lichnerowicz constraint system

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Abstract

We study the Einstein–Lichnerowicz constraint system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to the physics data when posed on the standard \(3\)-sphere.

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Acknowledgments

The two authors wish to thank Emmanuel Hebey for fruitful discussions during the preparation of this paper.

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Authors and Affiliations

  1. CNRS UMR 5208, Institut Camille Jordan, Université de Lyon 1, Lyon, France

    Olivier Druet

  2. Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, 95302, Cergy-Pontoise cedex, France

    Bruno Premoselli

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  1. Olivier Druet
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  2. Bruno Premoselli
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Correspondence to Olivier Druet.

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Druet, O., Premoselli, B. Stability of the Einstein–Lichnerowicz constraint system. Math. Ann. 362, 839–886 (2015). https://doi.org/10.1007/s00208-014-1145-0

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  • DOI: https://doi.org/10.1007/s00208-014-1145-0

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