Démonstration de la conjecture de la masse positive

On a compact Riemannian manifold (Vn,g)(Vn,g)(n>2)(n>2), when the conformal Laplacian L   is invertible, we show, under necessary hypotheses, that if the Green function GLGL of L   is of the form (here r=d(P,Q)r=d(P,Q)) GL(P,Q)=1/(n−2)ωn−1rn−2+H(P,Q)GL(P,Q)=1/(n−2)ωn−1rn−2+H(P,Q) with H(P,Q)H(P,Q) bounded on V, thenlimr→0r1−n∫∂BP(r)H(P,Q)dσ(Q)>0. Applications to the positive mass conjecture and to the C0C0 compactness of the set of the solutions of the Yamabe equation.