Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

TL;DR

This paper adapts an iterative method to prove the existence of many asymptotically hyperbolic solutions with non-constant mean curvature for the Einstein constraint equations on manifolds.

Contribution

It extends previous techniques to the asymptotically hyperbolic setting, demonstrating the existence of large sets of solutions with non-constant mean curvature.

Findings

Established existence of large sets of solutions

Extended iterative techniques to hyperbolic manifolds

Confirmed non-constant mean curvature solutions

Abstract

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.