Isospectral metrics on five-dimensional spheres

We construct isospectral pairs of Riemannian metrics on S-5 and on B-6, thus lowering by three the minimal dimension of spheres and balls on which such metrics have been constructed previously (S-n greater than or equal to8 and B-ngreater than or equal to9). We also construct continuous families of isospectral Riemannian metrics on S-7 and on B-8. In each of these examples, the metrics can be chosen equal to the standard metric outside certain subsets of arbitrarily small volume.