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

Scalar Flat Compactifications Of Poincar{\'e}-einstein Manifolds And Applications