Chinese Annals of Mathematics, Series B

, Volume 27, Issue 1, pp 31–52 | Cite as

The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*

  • Yvonne Choquet-Bruhat
  • James Isenberg
  • Daniel Pollack


By using the conformal method, solutions of the Einstein-scalar field gravitational constraint equations are obtained. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. The proofs are constructive and allow for arbitrary dimension (> 2) as well as low regularity initial data.


Einstein-scalar field Constraints Asymptotically Euclidian 

MR (2000) Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yvonne Choquet-Bruhat
    • 1
  • James Isenberg
    • 2
  • Daniel Pollack
    • 3
  1. 1.Academie des SciencesParis 06France
  2. 2.Department of MathematicsUniversity of OregonEugene, OR 97403USA
  3. 3.Department of MathematicsUniversity of WashingtonSeattle, WA 98195-4350USA

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