Towering Phenomena for the Yamabe Equation on Symmetric Manifolds

Abstract

Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ae<yen> 7. Assume M is symmetric with respect to a point xi (0) with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem We prove that for any k a a"center dot, there exists epsilon (k) > 0 such that for all epsilon a (0, epsilon (k) ) the problem (P (oee-) ) has a symmetric solution u (epsilon) , which looks like the superposition of k positive bubbles centered at the point xi (0) as epsilon -> 0. In particular, xi (0) is a towering blow-up point.