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Let $(M,g)$ be a compact conformally flat manifold of dimension $n\geq4$ withpositive scalar curvature. According to a positive mass theorem by Schoen andYau, the constant term in the development of the Green function of theconformal Laplacian is positive if $(M,g)$ is not conformally equivalent to thesphere. On spin manifolds, there is an elementary proof of this fact by Ammannand Humbert, based on a proof of Witten. Using differential forms instead ofspinors, we give an elementary proof on even dimensional manifolds, without anyother topological assumption.

Un th\'eor\`eme de la masse positive pour le probl\`eme de Yamabe en dimension paire