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A class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature
2009
Mathematical Research Letters
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a so-called global supersolution but does not require a global subsolution. As a consequence, we construct a class of solutions of the vacuum Einsten constraint equations with freely specified mean curvature, extending a recent result [16] which constructed similar
doi:10.4310/mrl.2009.v16.n4.a6
fatcat:shlgvlsewnfkbl4vpc2zj5whtq