2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35316We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. 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. Our proofs are constructive and allow for arbitrary dimension (>2) as well as low regularity initial data.31 pagesGeneral Relativity and Quantum CosmologyDifferential Geometrytext