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Solutions to scalar curvature equations have the property that all possibleblow-up points are isolated, at least in low dimensions. This property iscommonly used as the first step in the proofs of compactness. We show that thisresult becomes false for some arbitrarily small, smooth perturbations of thepotential.

Examples of non-isolated blow-up for perturbations of the scalar curvature equation on non locally conformally flat manifolds