Un théorème de la masse positive pour le problème de Yamabe en dimension paire

Let (M, g) be a compact conformally flat manifold of dimension n ≧ 4 with positive scalar curvature. According to a positive mass theorem by Schoen and Yau, the constant term in the development of the Green function of the conformal Laplacian is positive if (M, g) is not conformally equivalent to the sphere. On spin manifolds, there is an elementary proof of this fact by Ammann and Humbert, based on a proof of Witten. Using differential forms instead of spinors, we give an elementary proof on even dimensional manifolds, without any other topological assumption.