A continuity method to construct canonical metrics

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We introduce a new continuity method which provides an alternative way of carrying out the Analytic Minimal Model Program introduced by G. Tian and J. Song and G. Tian. This equation -- unlike the Ricci flow -- has the advantage of having Ricci curvature bounded from below along the deformation, so that the compactness theory of Cheeger-Colding-Tian for Kaehler manifolds and the partial C⁰-estimate, can be applied.