Abstract
The constraints equations of General Relativity are reduced on an initial maximal submanifold, by the use of conformai techniques, to a non-linear elliptic equation for the conformal factor φ. Some existence, uniqueness, and nonexistence theorems are proved for this equation, in the case of closed manifolds, and also for open manifolds (in particular for manifolds homeomorphic to ℝ3).
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Choquet-Bruhat, Y. Global solutions of the constraints equations on open and closed manifolds. Gen Relat Gravit 5, 49–60 (1974). https://doi.org/10.1007/BF00758074
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DOI: https://doi.org/10.1007/BF00758074