Integral Boundary Invariants for Conformally Compact Einstein Manifolds and Generalizations

In this article we investigate volume invariants on the boundary of conformally compact manifolds, subject to constant scalar curvature condition. This work is a generalization of that of R Graham, where the Einstein condition was considered. It is shown that the invariants under weakening to constant scalar curvature condition are different in general from those under Einstein condition. We then look at some cases of constant scalar curvature condition involving the measure of Chang, Gursky and Yang.