A limit equation criterion for applying the conformal method to asymptotically cylindrical initial data sets

Abstract

We prove that in a certain class of conformal data on an asymptotically cylindrical manifold, if the conformally decomposed Einstein constraint equations do not admit a solution, then one can always find a nontrivial solution to the limit equation first explored by Dahl, Gicquaud, and Humbert in [DGH11]. We also give an example of a Ricci curvature condition on the manifold which precludes the existence of a solution to this limit equation, showing that such a limit criterion can be a useful tool for studying the Einstein constraint equations on manifolds with asymptotically cylindrical ends.

21 pages

References in corpus (2)

• Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics
• Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

Cited by in corpus (1)

• Rough solutions of the Einstein Constraint Equations on Asymptotically Flat Manifolds without Near-CMC Conditions