Weak solutions to Monge-Amp\`ere type equations on compact Hermitian manifold with boundary

TL;DR

This paper establishes a bounded subsolution theorem for complex Monge-Ampère type equations on compact Hermitian manifolds with boundary, extending the understanding of solutions in complex geometry.

Contribution

It proves the bounded subsolution theorem for Monge-Ampère type equations with Radon measure right-hand side on Hermitian manifolds with boundary, a novel extension in complex analysis.

Findings

Established bounded subsolution theorem for complex Monge-Ampère equations

Extended theory to cases with Radon measure right-hand sides

Applied results to compact Hermitian manifolds with boundary

Abstract

We prove the bounded subsolution theorem for the complex Monge-Amp\`ere type equation, with the right hand side being a positive Radon measure, on a compact Hermitian manifold with boundary.