Abstract
While the set of constant mean curvature solutions of Einstein’s constraint equations is fairly well-understood, those solutions which have nonconstant mean curvature have resisted study. Here, we discuss a result obtained by the authors, and independently Choquet-Bruhat, which shows how to obtain a large set of nonconstant mean curvature solutions. In [1], a Leray-Schauder version of the proof of our existence theorem is presented. Here, we sketch a more constructive proof, which is based on sub and super solution theory.
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References
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© 1994 Springer Science+Business Media Dordrecht
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Isenberg, J., Moncrief, V. (1994). Some Results on Non Constant Mean Curvature Solutions of the Einstein Constraint Equations. In: Flato, M., Kerner, R., Lichnerowicz, A. (eds) Physics on Manifolds. Mathematical Physics Studies, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1938-2_21
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DOI: https://doi.org/10.1007/978-94-011-1938-2_21
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