The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*
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.
KeywordsEinstein-scalar field Constraints Asymptotically Euclidian
MR (2000) Subject Classification83C05
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