Weak Solutions to Complex Monge-Amp\`ere Equations on Compact K\"ahler Manifold

TL;DR

This paper proves a general existence theorem for complex Monge-Ampère equations on compact Kähler manifolds, advancing the understanding of solutions in complex differential geometry.

Contribution

It establishes a broad existence result for complex Monge-Ampère equations on compact Kähler manifolds, extending previous theoretical frameworks.

Findings

Existence of solutions to complex Monge-Ampère equations on compact Kähler manifolds.

Generalized conditions under which solutions exist.

Contributes to the theoretical foundation of complex differential geometry.

Abstract

We show a general existence theorem to the complex Monge-Amp\`ere type equation on compact K\"ahler manifolds.