The Constraint Equations in the Presence of a Scalar Field - the Case of the Conformal Method with Volumetric Drift

TL;DR

This paper proves the existence of solutions to the conformal constraint equations with a scalar field in low dimensions, under smallness conditions, extending Maxwell's recent conformal method.

Contribution

It introduces existence results for the conformal constraint equations with scalar fields, incorporating volumetric drift, in low-dimensional settings.

Findings

Existence of solutions established in low dimensions.

Results depend on smallness assumptions of scalar field parameters.

Extends Maxwell's conformal method to include scalar fields.

Abstract

In this paper we establish the existence in low dimensions of solutions to the constraint equations in the case of the conformal system recently proposed by David Maxwell, with the added presence of a scalar field and under suitable smallness assumptions on its parameters.