On Multiplier Hermitian Structures on Compact Kahler Manifolds

TL;DR

This paper generalizes a Moser-Trudinger type inequality to multiplier Hermitian structures on compact Kahler manifolds, extending concepts related to Kahler-Einstein metrics.

Contribution

It introduces a generalization of key inequalities to a broader class of structures on Kahler manifolds, expanding the theoretical framework.

Findings

Generalized Moser-Trudinger inequality for multiplier Hermitian structures

Extended the theoretical understanding of metrics similar to Kahler-Einstein

Provided new tools for studying Kahler geometry

Abstract

Mabuchi introduced multiplier Hermitian structures on compact Kahler manifolds and defined metrics similar to Kahler-Einstein metrics under these structures. In this note we generalize the inequality of Moser-Trudinger type on Kahler-Einstein manifolds to this case.