ISOPARAMETRIC HYPERSURFACES AND METRICS OF CONSTANT SCALAR CURVATURE

We showed the existence of non-radial solutions of the equation Delta u - Delta u + lambda u(q) = 0 on the round sphere S-m, for q < (m + 2)/(m + 2), and study the number of such solutions in terms of lambda. We show that for any isoparametric hypersurface M subset of S-m there are solutions such that M is a regular level set (and the number of such solutions increases with lambda). We also show similar results for isoparametric hypersurfaces in general Riemannian manifolds. These solutions give multiplicity results for metrics of constant scalar curvature on conformal classes of Riemannian products.