The Dirichlet problem for Monge-Amp\`ere type equations on Hermitian manifolds

TL;DR

This paper addresses solving the Dirichlet problem for Monge-Ampère type equations involving (n-1)-plurisubharmonic functions on Hermitian manifolds, advancing the understanding of complex geometric PDEs.

Contribution

It introduces a method to solve the Dirichlet problem for Monge-Ampère equations on Hermitian manifolds for (n-1)-plurisubharmonic functions, extending previous results.

Findings

Existence of solutions to the Dirichlet problem established.

Method applicable to a broad class of Hermitian manifolds.

Provides new insights into complex Monge-Ampère equations.

Abstract

In this paper, we solve the Dirichlet problem for Monge-Amp\`ere type equations for $(n-1)$-plurisubharmonic functions on Hermitian manifolds.