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

Dan Coman, Vincent Guedj, Ahmed Zeriahi

Research output: Contribution to journalArticle

16 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)393-418
Number of pages26
JournalMathematische Zeitschrift
Volume259
Issue number2
DOIs
StatePublished - Jun 2008

ASJC Scopus subject areas

  • Mathematics(all)

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