科研之友
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摘要
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.
- 出版日期2015-7
