METRICS OF CONSTANT SCALAR CURVATURE CONFORMAL TO RIEMANNIAN PRODUCTS

摘要

We consider the conformal class of the Riemannian product go +g,where go is the constant curvature metric on Sm and g is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of constant scalar curvature in the conformal class grows at least linearly with respect to the square root of the scalar curvature of g. This is obtained by studying radial solutions of the equation Au — Au + Eu~p 0 on S' and the number of solutions in terms of E