Solution complète de la C0 compacité de l'ensemble des solutions de l'équation de Yamabe

On a compact Riemannian manifold (Vn,g) (n>2), a long-standing question is: Does the set of the solutions of the Yamabe equation compact in C0? There are three cases in the Yamabe problem (see Aubin [T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998]) according to the sign of the inf of the Yamabe functional. We prove the C0 compactness of the set of the solutions of the Yamabe equation (except on the sphere) in the positive case, the only case which makes difficulties.