Abstract :
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.
