Addendum: Conformal Deformation of a Riemannian Metric to a Scalar Flat Metric with Constant Mean Curvature

is finite. On the other hand the argument at the beginning of Proposition 2.1 in E shows that if Al (B) is finite then Q(M, OM) is finite. Jin Zhiren pointed out to me that the Sobolev quotient Q(M, O9M) can be -oo. This is the case if we delete a small geodesic ball on a compact manifold without boundary with negative scalar curvature. More generally the Sobolev quotient is -oo if the first eigenvalue for the conformal Laplacian, with respect to Dirichlet boundary condition, is negative. In order to see that let p1 be the first eigenfunction for the problem