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

Abstract: 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. This is joint work with S lawomir Ko lodziej.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

2021 Pacific Rim Complex & Symplectic Geometry Conference