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Monotonicity of
nonpluripolar products and complex Monge–Ampère equations
with prescribed singularity
Tamás Darvas, Eleonora Di Nezza and Chinh H. Lu |
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Vol. 11 (2018), No. 8, 2049–2087
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DOI: 10.2140/apde.2018.11.2049
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Abstract |
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We establish the monotonicity property for the mass of nonpluripolar products on compact Kähler manifolds, and we initiate the study of complex Monge–Ampère-type equations with prescribed singularity type. Using the variational method of Berman, Boucksom, Guedj and Zeriahi we prove existence and uniqueness of solutions with small unbounded locus. We give applications to Kähler–Einstein metrics with prescribed singularity, and we show that the log-concavity property holds for nonpluripolar products with small unbounded locus. |
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Keywords
Monge–Ampère equation, variational approach, pluripotential
theory
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Mathematical Subject Classification 2010
Primary: 32Q15, 32U05, 32W20
Secondary: 32Q20
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Milestones
Received: 27 June 2017
Revised: 4 February 2018
Accepted: 10 April 2018
Published: 6 June 2018
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Authors |
| Tamás Darvas | |
| Department of Mathematics University of Maryland College Park, MD United States |
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| Eleonora Di Nezza | |
| Institut des Hautes Études
Scientifiques Université Paris-Saclay Bures sur Yvette France |
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| Chinh H. Lu | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud CNRS Université Paris-Saclay Orsay France |
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