Principe de recollement des équations des contraintes en relativité générale
[Gluing principle for the constraint equations in general relativity]
Séminaire de théorie spectrale et géométrie, Volume 30 (2011-2012), pp. 21-45.

The “gluing” method to find solutions to the relativistic constraint equations is reviewed. In particular, we describe the Corvino-Schoen method to construct families of solutions on a non-compact manifold with prescribed geometry on an asymptotic end, with emphasis on the “non-localized” gluing. We then provide a list of results obtained by various authors using such techniques, including the question of gluing Riemannian metrics while preserving their (constant) scalar curvature. We eventually give some applications in geometric analysis and in general relativity.

La méthode de «  recollement  » permettant de trouver des solutions des équations des contraintes relativistes est décrite. En particulier, on expose la méthode de Corvino-Schoen pour construire des familles de solutions sur une variété non-compacte avec géométrie prescrite sur un bout asymptotique, en insistant sur le recollement «  non-localisé  ». Une liste de résultats obtenus par divers auteurs à partir de telles techniques est alors fournie, incluant la question du recollement de métriques riemanniennes en préservant leur courbure scalaire (constante). On donne enfin certaines applications en analyse géométrique et en relativité générale.

DOI: 10.5802/tsg.289
Classification: 58J05, 83C05, 53C21, 53C50
Mot clés : relativité générale, formulation de Cauchy, équations des contraintes, recollement.
Keywords: general relativity, Cauchy formulation, constraint equations, gluing.
Cortier, Julien 1

1 Institut des Hautes Études Scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France
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Cortier, Julien. Principe de recollement des équations des contraintes en relativité générale. Séminaire de théorie spectrale et géométrie, Volume 30 (2011-2012), pp. 21-45. doi : 10.5802/tsg.289. http://archive.numdam.org/articles/10.5802/tsg.289/

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