Blow-up phenomena for the Yamabe equation

Abstract

Let ( M , g ) (M,g) be a compact Riemannian manifold of dimension n ≥ 3 n \geq 3 . A well-known conjecture states that the set of constant scalar curvature metrics in the conformal class of g g is compact unless ( M , g ) (M,g) is conformally equivalent to the round sphere. In this paper, we construct counterexamples to this conjecture in dimensions n ≥ 52 n \geq 52 .