Abstract
We prove that in a certain class of conformal data on a manifold with ends of cylindrical type, 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 et al. (Duke Math J 161(14):2669–2798, 2012). We also give an example of a Ricci curvature condition on the manifold which precludes the existence of a solution to this limit equation. This shows that the limit equation criterion can be a useful tool for proving the existence of solutions to the Einstein constraint equations on manifolds with ends of cylindrical type.
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Communicated by James A. Isenberg.
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Dilts, J., Leach, J. A Limit Equation Criterion for Solving the Einstein Constraint Equations on Manifolds with Ends of Cylindrical Type. Ann. Henri Poincaré 16, 1583–1607 (2015). https://doi.org/10.1007/s00023-014-0357-x
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DOI: https://doi.org/10.1007/s00023-014-0357-x