Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 8 (2018), 2049-2087.

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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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.

Article information

Anal. PDE, Volume 11, Number 8 (2018), 2049-2087.

Received: 27 June 2017
Revised: 4 February 2018
Accepted: 10 April 2018
First available in Project Euclid: 15 January 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q15: Kähler manifolds 32U05: Plurisubharmonic functions and generalizations [See also 31C10] 32W20: Complex Monge-Ampère operators
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]

Monge–Ampère equation variational approach pluripotential theory


Darvas, Tamás; Di Nezza, Eleonora; Lu, Chinh H. Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity. Anal. PDE 11 (2018), no. 8, 2049--2087. doi:10.2140/apde.2018.11.2049.

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