Scalar Curvature and the Einstein Constraint Equations

Details Scalar Curvature and the Einstein Constraint Equations Scalar Curvature and the Einstein Constraint Equations

2011-02-24

arxiv.org/abs/1102.5050v1

Mathematics

Differential Geometry

39 pages. To appear in the volume "Surveys in Geometric Analysis and Relativity celebrating Richard Schoen's 60th birthday."

Scientific paper

We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the geometry of the center of mass of such solutions. We also review methods to construct solutions to the constraint equations, including the conformal method, as well as gluing techniques for which it is important to understand both conformal and non-conformal deformations of the scalar curvature.

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