Continuous solutions to Monge-Amp`ere equations on Hermitian manifolds for measures dominated by capacity


Abstract in English

We prove the existence of a continuous quasi-plurisubharmonic solution to the Monge-Amp`ere equation on a compact Hermitian manifold for a very general measre on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh-Nguyen-Sibony. As a consequence, we give a characterization of measures admitting Holder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh-Nguyen.

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