Monge-Ampere type equations on compact Hermitian manifolds with bounded mass property

TL;DR

This paper investigates complex Monge-Ampere equations on compact Hermitian manifolds with bounded mass, providing existence criteria for solutions with prescribed singularities and extending stability results to this setting.

Contribution

It introduces new existence criteria for solutions to Monge-Ampere equations with singularities on Hermitian manifolds and extends stability analysis to this broader context.

Findings

Existence of solutions with prescribed singularities on Hermitian manifolds.

Criteria for the existence of rooftop envelopes.

Extension of stability results to non-Kahler Hermitian manifolds.

Abstract

In this paper, we study possibly non-closed big (1, 1)-forms on a compact Hermitian manifold satisfying the bounded mass property. We propose several criteria for the existence of rooftop envelopes. As applications, we establish the existence of solutions to complex Monge-Ampere type equations with prescribed singularities, allowing for non-pluripolar measures on the right-hand side. We also obtain stability results when singularity types vary, by extending the Darvas-Di Nezza-Lu distance to the Hermitian context.