Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

Details Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

2007-10-03

arxiv.org/abs/0710.0725v2

Class.Quant.Grav.25:075009,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

10.1088/0264-9381/25/7/075009

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.

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