2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126528We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced to an extremal problem for the harmonic extension of functions and the related nonlinear integral equation is discussed.23 pagesAnalysis of PDEsDifferential Geometry45G05, 53A30text