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Stability and instability for Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

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Abstract

We investigate stability issues for Einstein-scalar field Lichnerowicz equations in the inhomogeneous context of a compact Riemannian manifold. We prove that stability holds true when the dimension n is such that n ≤ 5 and fails to hold in general when n ≥ 6.

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Authors and Affiliations

  1. Département de Mathématiques-UMPA, Ecole normale supérieure de Lyon, 46 allée d’Italie, 69364, Lyon Cedex 07, France

    Olivier Druet

  2. Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France

    Emmanuel Hebey

Authors
  1. Olivier Druet
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  2. Emmanuel Hebey
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Correspondence to Emmanuel Hebey.

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Druet, O., Hebey, E. Stability and instability for Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds. Math. Z. 263, 33–67 (2009). https://doi.org/10.1007/s00209-008-0409-3

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  • DOI: https://doi.org/10.1007/s00209-008-0409-3

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