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 -