2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154041We review recent compactness and non-compactness results for the Yamabe equation. We also discuss the asymptotic behavior of the parabolic Yamabe flow.to appear in Surveys in Differential GeometryDifferential GeometryAnalysis of PDEsOn the conformal scalar curvature equation and related problemstext