The Einstein-scalar field constraints on asymptotically Euclidean manifolds (Q2431978)

The authors study the Einstein equations on an \(n+1\) dimensional manifold, with source a scalar field of a non-specified potential. By using the conformal method, they obtain an elliptic system for the constraints satisfied by the initial data of the Einstein-scalar field system. They also prove, under a low regularity hypothesis, some existence and uniqueness theorems for their solutions in the case where the \(n\) dimensional manifold on which the initial data are defined is asymptotically Euclidean.