**Choquet-bruhat, Y., A. E. Fischer and J. E. Marsden
**

In *Isolated Gravitating Systems in General Relativity*, Italian Physical Society, (J. Ehlers, ed.), (1979), 396-456

This paper discusses some recent results on the related problems of positivity of mass and the existence of maximal spacelike hypersurfaces
for asymptotically flat space-times. If
*k*_{}
denotes the second fundamental form of
, then
is called maximal if
tr*k*_{} = 0
, has constant mean extrinsic curvature if
tr*k*_{} = const
on
, and is a moment of time-symmetry if
*k*_{} = 0
.

We will give a certain amount of background material in order to keep the exposition self-contained. However, we so assume familiarity with the ADM formalism.

We will give a certain amount of background material in order to keep the exposition self-contained. However, we so assume familiarity with the ADM formalism.