  We examine here the space of conformally compact metrics $g$ on the interior
of a compact manifold with boundary which have the property that the $k^{th}$
elementary symmetric function of the Schouten tensor $A_g$ is constant. When
$k=1$ this is equivalent to the familiar Yamabe problem, and the corresponding
metrics are complete with constant negative scalar curvature. We show for every
$k$ that the deformation theory for this problem is unobstructed, so in
particular the set of conformal classes containing a solution of any one of
these equations is open in the space of all conformal classes. We then observe
that the common intersection of these solution spaces coincides with the space
of conformally compact Einstein metrics, and hence this space is a finite
intersection of closed analytic submanifolds.
