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Keywords:
$\omega $-plurisubharmonic function; weakly convergent; complex Monge-Ampère operator; compact Hermitian manifold; convergence in capacity; weak solution of complex Monge-Ampère equation
$\omega $-plurisubharmonic function; weakly convergent; complex Monge-Ampère operator; compact Hermitian manifold; convergence in capacity; weak solution of complex Monge-Ampère equation
Summary:
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.
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