Envelope Approach to Degenerate Complex Monge-Amp\`ere Equations on compact K\"ahler manifold

TL;DR

This paper introduces a classical Perron envelope method to establish a general existence theorem for degenerate complex Monge-Ampère equations on compact Kähler manifolds, advancing the understanding of such complex geometric PDEs.

Contribution

It applies the Perron envelope technique to prove existence results for degenerate complex Monge-Ampère equations on compact Kähler manifolds, a novel approach in this context.

Findings

Proved a general existence theorem for degenerate complex Monge-Ampère equations.

Extended classical Perron envelope method to complex geometric PDEs.

Provided new tools for solving degenerate Monge-Ampère equations on Kähler manifolds.

Abstract

We shall use the classical Perron envelope method to show a general existence theorem to degenerate complex Monge-Amp\`ere type equations on compact K\"ahler manifolds.