# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsarXiv subject: Differential Geometry (math.DG)mathscidoc:2005.03004

In this paper, we derive estimates for scalar curvature type equations with more singular right hand side. As an application, we prove Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK when \$Aut_0(M,J)\neq0\$. Moreover, we show that when \$Aut_0(M,J)\neq0\$, the properness of \$K\$-energy with respect to a suitably defined distance implies the existence of cscK.
cscK metrics, general cscK type equations, apriori estimates
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