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Rough Solutions of the Einstein Constraint Equations on Compact Manifolds

David Maxwell
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Abstract

We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in $H^s$ where $s>3/2$. The constant mean curvature (CMC) conformal method leads to a construction of all CMC initial data with this level of regularity. These results extend a construction from Ma04 that treated the asymptotically Euclidean case.

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David Maxwell. 2005-06-15. Rough Solutions of the Einstein Constraint Equations on Compact Manifolds. https://doi.org/10.1142/s021989160500049x

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