An Inequality for Mixed Monge-Amp\`ere measures

TL;DR

This paper generalizes an inequality related to mixed Monge-Ampère measures, providing sharp assumptions and extending the results to compact Kähler manifolds, thereby advancing the understanding of complex geometric inequalities.

Contribution

It introduces a generalized inequality for mixed Monge-Ampère measures with sharp assumptions and discusses its extension to compact Kähler manifolds.

Findings

Established a generalized inequality for mixed Monge-Ampère measures.

Provided an example demonstrating the sharpness of the assumptions.

Extended the inequality to the setting of compact Kähler manifolds.

Abstract

We generalize an inequality for mixed Monge-Amp\`ere measures. We also give an example that shows that our assumptions are sharp. The corresponding result in the setting of compact K\"ahler manifold is also discussed.