  We study boundary regularity for conformally compact Einstein metrics in even
dimensions by generalizing the ideas of Michael Anderson. Our method of
approach is to view the vanishing of the Ambient Obstruction tensor as an nth
order system of equations for the components of a compactification of the given
metric. This, together with boundary conditions that the compactification is
shown to satisfy provide enough information to apply classical boundary
regularity results. These results then provide local and global versions of
finite boundary regularity for the components of the compactification.
