Constant scalar curvature Kahler metric and K-energy

TL;DR

This paper proves that in an integral Kähler class, the existence of a constant scalar curvature Kähler metric guarantees it minimizes the K-energy, without requiring the automorphism group to be discrete.

Contribution

It extends Donaldson's method to show that constant scalar curvature Kähler metrics minimize K-energy without automorphism group restrictions.

Findings

Constant scalar curvature Kähler metric minimizes K-energy.

No assumption of discrete automorphism group needed.

Method based on Donaldson's approach.

Abstract

Based on Donaldson's method, we prove that, for an integral Kahler class, when there is a Kahler metric of constant scalar curvature, then it minimizes the K-energy. We do not assume that the automorphism group is discrete.