Solutions to the Einstein-scalar field constraint equations with a small TT-tensor

TL;DR

This paper proves a new result for Einstein-scalar field constraint equations on compact manifolds, extending previous work to cases with small TT-tensors and positive Yamabe invariant.

Contribution

It introduces a far-from-constant mean curvature (CMC) solution approach for Einstein-scalar field constraints with small TT-tensors, expanding the theoretical understanding.

Findings

Established existence of solutions with small TT-tensors

Extended previous CMC results to non-CMC cases

Applied to manifolds with positive Yamabe invariant

Abstract

In this paper, we prove a far-from-CMC result similar to the ones obtained by Holst, Nagy, Tsogtgerel and Maxwell for the conformal Einstein-scalar field constraint equations on compact Riemannian manifolds with positive (modified) Yamabe invariant.