HOLDER CONTINUOUS SOLUTIONS OF THE MONGE-AMPERE EQUATION ON COMPACT HERMITIAN MANIFOLDS

Abstract

We show that a positive Borel measure of positive finite total mass, on a compact Hermitian manifold, admits a Holder continuous quasi-plurisubharmonic solution to the Monge-Ampere equation if and only if it is dominated locally by Monge-Ampere measures of Holder continuous plurisubharmonic functions.