Continuity of the complex Monge-Ampère operator on compact Hermitian manifolds

Abstract

In this note, we establish several results concerning the continuity (or weak convergence) of the complex Monge-Ampère operator on compact Hermitian manifolds. At the end of this note, we find a weak solution of the complex Monge-Ampère equation on a compact Hermitian manifold under the assumption of the existence of a smooth subsolution.

13 pages, accepted in Czechoslovak Mathematical Journal