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

2007/05/31 by Dan Coman, Coman, Dan, Vincent Guedj +3
Mathematics · #32Q15 #32U15 #32W20 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.0705.4529

openalex publication_date 2007/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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