scholarly journals Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature

2015 ◽  
Vol 17 (8) ◽  
pp. 2237-2263 ◽  
Author(s):  
The Cang Nguyen
Keyword(s):  
Fixed Point ◽  
Mean Curvature ◽  
Fixed Point Theorems ◽  
Constant Mean Curvature ◽  
Constraint Equations ◽  
Einstein Constraint Equations

scholarly journals ROUGH SOLUTIONS OF THE EINSTEIN CONSTRAINT EQUATIONS ON COMPACT MANIFOLDS

2005 ◽  
Vol 02 (02) ◽  
pp. 521-546 ◽  
Author(s):  
DAVID MAXWELL
Keyword(s):  
Initial Data ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Compact Manifolds ◽  
Euclidean Case ◽  
Low Regularity ◽  
Constraint Equations ◽  
Conformal Method ◽  
Low Regularity Solutions ◽  
Einstein Constraint Equations

We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in Hs 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 [10] that treated the asymptotically Euclidean case.

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