Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds

Abstract

In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with restrictions on the size of the transverse-traceless data and the non-gravitational field data, while the second assumes a near-CMC condition, with no other restrictions.

arXiv comment8 pages

References in corpus (5)

• Einstein Constraints on Asymptotically Euclidean Manifolds
• Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
• Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions
• Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics
• A far-from-CMC existence result for the constraint equations on manifolds with ends of cylindrical type

Cited by in corpus (4)

• On the backward stability of the Schwarzschild black hole singularity
• High-frequency solutions to the constraint equations
• Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal Method
• Einstein-type elliptic systems