Domains of definition of Monge-Ampère operators on compact Kähler manifolds

Abstract

Let $(X,\omega )$ be a compact Kähler manifold. We introduce and study the largest set $DMA(X,\omega )$ of $\omega$-plurisubharmonic (psh) functions on which the complex Monge-Ampère operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set $PSH(X,\om)$ of all $\om$-psh functions. We prove that certain twisted Monge-Ampère operators are well defined for all $\omega$-psh functions. As a consequence, any $\om$-psh function with slightly attenuated singularities has finite weighted Monge-Ampère energy.

References in corpus (1)

• The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds