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

Dan Coman; Vincent Guedj; Ahmed Zeriahi

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arXiv · 0705.4529

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

Dan Coman·Vincent Guedj·Ahmed Zeriahi

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Abstract

Let $(X,ω)$ be a compact Kähler manifold. We introduce and study the largest set $DMA(X,ω)$ of $ω$-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 $ω$-psh functions. As a consequence, any $\om$-psh function with slightly attenuated singularities has finite weighted Monge-Ampère energy.

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BibTeX RIS

Dan Coman, Vincent Guedj, Ahmed Zeriahi. 2007-05-31. Domains of definition of Monge-Ampère operators on compact Kähler manifolds. https://arxiv.org/abs/0705.4529

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