| Softcover ISBN: | 978-2-37905-207-1 |
| Product Code: | SMFMEM/184 |
| List Price: | $108.00 |
| AMS Member Price: | $86.40 |
| Softcover ISBN: | 978-2-37905-207-1 |
| Product Code: | SMFMEM/184 |
| List Price: | $108.00 |
| AMS Member Price: | $86.40 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 184; 2025; 212 ppMSC: Primary 83; 35
In this paper the author proves the nonlinear global stability of Minkowski space in the framework of the spatial-characteristic Cauchy problem for the Einstein equations in vacuum. The spatial-characteristic initial data are prescribed on a 3-disk and on the future-complete zero hypersurface emanating from the boundary of this disk. The author's result extends the original result proved by Christodoulou and Klainerman for which the initial data are prescribed on a spatial hyperplane.
The proof is based on the vector field method and the bootstrap argument introduced in Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the characteristic-space framework. In particular, the author uses vertex-prescribed light cones, boundary-prescribed maximal spatial hypersurfaces, and global harmonic coordinates on Riemannian 3-disks.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
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In this paper the author proves the nonlinear global stability of Minkowski space in the framework of the spatial-characteristic Cauchy problem for the Einstein equations in vacuum. The spatial-characteristic initial data are prescribed on a 3-disk and on the future-complete zero hypersurface emanating from the boundary of this disk. The author's result extends the original result proved by Christodoulou and Klainerman for which the initial data are prescribed on a spatial hyperplane.
The proof is based on the vector field method and the bootstrap argument introduced in Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the characteristic-space framework. In particular, the author uses vertex-prescribed light cones, boundary-prescribed maximal spatial hypersurfaces, and global harmonic coordinates on Riemannian 3-disks.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
