2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231235Let (M,g) be a compact Riemannian manifold of dimension n \geq 3. The Compactness Conjecture asserts that the set of constant scalar curvature metrics in the conformal class of g is compact unless (M,g) is conformally equivalent to the round sphere. In this paper, we construct counterexamples to this conjecture in dimensions n \geq 52.Published paperDifferential GeometryAnalysis of PDEstext