2014/01/21 by James Dilts, Dilts, James, Jeremy Leach +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis #gr-qc #math.AP
paper · pdf · doi:10.48550/arxiv.1401.5369
21 pages
arxiv created 2014/01/21 · openalex publication_date 2014/01/21 · arxiv updated 2014/01/22 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
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.