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, ω) of all ω-psh functions. We prove that certain twisted Monge-Ampère operators are well defined for all ω-psh functions. As a consequence, any ω-psh function with slightly attenuated singularities has finite weighted Monge-Ampère energy.
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Dan Coman was partially supported by the NSF Grant DMS 0500563.
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Coman, D., Guedj, V. & Zeriahi, A. Domains of definition of Monge-Ampère operators on compact Kähler manifolds. Math. Z. 259, 393–418 (2008). https://doi.org/10.1007/s00209-007-0233-1
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DOI: https://doi.org/10.1007/s00209-007-0233-1