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

Abstract

Let $(M,g)$ be a compact conformally flat manifold of dimension $n\ge 4$ 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.

arXiv comment6 pages, in french