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

Allen, Paul T.; Clausen, Adam; Isenberg, James

doi:1088/0264-9381/25/7/075009

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

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Allen, Paul T.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Allen, P. T., Clausen, A., & Isenberg, J. (2008). Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics. Classical and Quantum Gravity, 25(7): 075009. doi:1088/0264-9381/25/7/075009.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-62CD-6

Abstract

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.