Yvonne Choquet-Bruhat

Global aspects of the Cauchy problem in general relativity

It is shown that, given any set of initial data for Einsteins equations which satisfy the constraint conditions, there exists a development of that data which is maximal in the sense that it is an extension of every other development. These maximal developments form a well-defined class of solutions of Einsteins equations. Any solution of Einsteins equations which has a Cauchy surface may be embedded in exactly one such maximal development.

Einstein constraints on asymptotically Euclidean manifolds

We consider the Einstein constraints on asymptotically euclidean manifolds

Future complete Einsteinian space times with U(1) isometry group

M

Future global in time Einsteinian spacetimes with U(1) isometry group

of dimension

Hyperbolicity of the 3 + 1 System of Einstein Equations

n \geq 3

Solution of the local mass problem in general relativity

with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.

Existence, uniqueness, and local stability for the Einstein-Maxwell-Boltzman system

Abstract We prove that spacetimes satisfying the vacuum Einstein equations on a manifold of the form Σ× U (1)× R , where Σ is a compact surface of genus G>1 and where the Cauchy data is invariant with respect to U(1) and sufficiently small exist for an infinite proper time in the expanding direction.

The Cauchy problem for stringy gravity

Abstract. We prove that spacetimes satisfying the vacuum Einstein equations on a manifold of the form¶

Einstein constraints on compact n-dimensional manifolds

\Sigma \times U(1) \times R

Einstein and Yang-Mills theories in hyperbolic form without gauge fixing

where