  We derive an integral inequality between the mean curvature and the scalar
curvature of the boundary of any scalar flat conformal compactifications of
Poincar{\'e}-Einstein manifolds. As a first consequence , we obtain a sharp
lower bound for the first eigenvalue of the conformal half-Laplacian of the
boundary of such manifolds. Secondly, a new upper bound for the renormalized
volume is given in the four dimensional setting. Finally, some estimates on the
first eigenvalues of Dirac operators are also deduced.
