On the constant scalar curvature Kähler metrics, general automorphism group

الأصل · EN

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 Aut₀(M,J)≠0. Moreover, we also show that when Aut₀(M,J)≠0, the properness of K-energy with respect to a suitably defined distance implies the existence of cscK.