  Let (M,g) be a compact Riemannian manifold of dimension >2. We show that
there is a metric h conformal to g and of volume 1 such that the first positive
eigenvalue the conformal Laplacian with repect to h is arbitrarily large. A
similar statement is proven for the first positive eigenvalue of the Dirac
operator on a spin manifold of dimension >1.

Differential Geometry