A Limit Equation Criterion for Solving the Einstein Constraint Equations on Manifolds with Ends of Cylindrical Type

Annales Henri Poincaré ◽

10.1007/s00023-014-0357-x ◽

2014 ◽

Vol 16 (7) ◽

pp. 1583-1607 ◽

Author(s):

James Dilts ◽

Jeremy Leach

Keyword(s):

Limit Equation ◽

Constraint Equations ◽

Einstein Constraint Equations

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A limit equation associated to the solvability of the vacuum Einstein constraint equations by using the conformal method

Duke Mathematical Journal ◽

10.1215/00127094-1813182 ◽

2012 ◽

Vol 161 (14) ◽

pp. 2669-2697 ◽

Author(s):

Mattias Dahl ◽

Romain Gicquaud ◽

Emmanuel Humbert

Keyword(s):

Limit Equation ◽

Constraint Equations ◽

Conformal Method ◽

Einstein Constraint Equations

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Non-constant mean curvature trumpet solutions for the Einstein constraint equations

Classical and Quantum Gravity ◽

10.1088/0264-9381/33/14/145001 ◽

2016 ◽

Vol 33 (14) ◽

pp. 145001

Author(s):

Jeremy Leach

Keyword(s):

Mean Curvature ◽

Constant Mean Curvature ◽

Constraint Equations ◽

Einstein Constraint Equations

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A set of nonconstant mean curvature solutions of the Einstein constraint equations on closed manifolds

Classical and Quantum Gravity ◽

10.1088/0264-9381/13/7/015 ◽

1996 ◽

Vol 13 (7) ◽

pp. 1819-1847 ◽

Author(s):

James Isenberg ◽

Vincent Moncrief

Keyword(s):

Mean Curvature ◽

Constraint Equations ◽

Einstein Constraint Equations

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Linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold

Journal of Mathematical Physics ◽

10.1063/1.3393914 ◽

2010 ◽

Vol 51 (7) ◽

pp. 072501 ◽

Author(s):

Romain Gicquaud

Keyword(s):

Hyperbolic Manifold ◽

Constraint Equations ◽

Asymptotically Hyperbolic Manifold ◽

Linearization Stability ◽

Einstein Constraint Equations ◽

Asymptotically Hyperbolic

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

Annales Henri Poincaré ◽

10.1007/s00023-015-0446-5 ◽

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

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Generalized gluing for Einstein constraint equations

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-008-0191-4 ◽

2008 ◽

Vol 34 (4) ◽

pp. 453-473 ◽

Author(s):

Lorenzo Mazzieri

Keyword(s):

Constraint Equations ◽

Einstein Constraint Equations

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A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold

Communications in Mathematical Physics ◽

10.1007/s00220-012-1420-4 ◽

2012 ◽

Vol 310 (3) ◽

pp. 705-763 ◽

Author(s):

Romain Gicquaud ◽

Anna Sakovich

Keyword(s):

Large Class ◽

Mean Curvature ◽

Constant Mean Curvature ◽

Hyperbolic Manifold ◽

Constraint Equations ◽

Asymptotically Hyperbolic Manifold ◽

Einstein Constraint Equations ◽

Asymptotically Hyperbolic

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Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

Classical and Quantum Gravity ◽

10.1088/0264-9381/32/2/025006 ◽

2014 ◽

Vol 32 (2) ◽

pp. 025006 ◽

Author(s):

Michael Holst ◽

Caleb Meier

Keyword(s):

Apparent Horizon ◽

Constraint Equations ◽

Einstein Constraint Equations

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Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

Communications in Mathematical Physics ◽

10.1007/s00220-017-3004-9 ◽

2017 ◽

Vol 357 (2) ◽

pp. 467-517

Author(s):

Michael Holst ◽

Caleb Meier ◽

G. Tsogtgerel

Keyword(s):

Apparent Horizon ◽

Compact Manifolds ◽

Constraint Equations ◽

Einstein Constraint Equations

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Manifolds with a circle action and the Einstein constraint equations

Differential Geometry and Mathematical Physics - Contemporary Mathematics ◽

10.1090/conm/170/01750 ◽

1994 ◽

pp. 149-154

Author(s):

James Isenberg ◽

Vincent Moncrief

Keyword(s):

Circle Action ◽

Constraint Equations ◽

Einstein Constraint Equations

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