A criterion for the properness of the K-energy in a general Kahler class (II)

TL;DR

This paper establishes criteria for the properness of the K-energy in general Kähler classes, addressing a question by Song-Weinkove and extending previous results to modified K-energy related to extremal Kähler metrics.

Contribution

It provides new criteria for the properness of K-energy in arbitrary dimensions and extends these results to modified K-energy for extremal Kähler metrics.

Findings

Criteria for properness of K-energy in general Kähler classes

Extension of properness results to modified K-energy

Answers a question posed by Song-Weinkove

Abstract

In this paper, we give a result on the properness of the K-energy, which answers a question of Song-Weinkove in any dimensions. Moreover, we extend our previous result on the properness of K-energy to the case of modified K-energy associated to extremal Kahler metrics.