Démonstration de la conjecture de la masse positive

On a compact Riemannian manifold (Vn,g) (n>2), when the conformal Laplacian L is invertible, we show, under necessary hypotheses, that if the Green function GL of L is of the form (here r = d(P,Q)) GL(P,Q) = 1/(n− 2)ωn−1rn−2 + H(P,Q) with H(P,Q) bounded on V , then lim r→0 r1−n ∂BP (r) H(P,Q)dσ(Q)>0. Applications to the positive mass conjecture and to the C0 compactness of the set of the solutions of the Yamabe equation. © 2006 Elsevier Inc. All rights reserved.