TY - JOUR

T1 - Domains of definition of Monge-Ampère operators on compact Kähler manifolds

AU - Coman, Dan

AU - Guedj, Vincent

AU - Zeriahi, Ahmed

N1 - Funding Information:
Dan Coman was partially supported by the NSF Grant DMS 0500563.

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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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U2 - 10.1007/s00209-007-0233-1

DO - 10.1007/s00209-007-0233-1

M3 - Article

AN - SCOPUS:43349096973

SN - 0025-5874

VL - 259

SP - 393

EP - 418

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 2

ER -