On the constant scalar curvature Kähler metrics, general automorphism group

Abstract

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 $Au{t}_0(M,J)\ne 0$. Moreover, we also show that when $Au{t}_0(M,J)\ne 0$, the properness of $K$-energy with respect to a suitably defined distance implies the existence of cscK.

References in corpus (2)

• On deformation of extremal metrics
• On the existence of constant scalar curvature Kähler metric: a new perspective

Cited by in corpus (5)

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• A uniform version of the Yau-Tian-Donaldson correspondence for extremal Kähler metrics on polarized toric manifolds
• Mahler measures, Stable Pairs, and the Global coercive estimate for the Mabuchi Functional
• Faltings Heights, Igusa Local Zeta Functions, and the Stability Conjectures in Kahler Geometry I