Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity

Abstract

We establish the monotonicity property for the mass of non-pluripolar products on compact Kahler manifolds, and we initiate the study of complex Monge-Ampere type equations with prescribed singularity type. Using the variational method of Berman-Boucksom-Guedj-Zeriahi we prove existence and uniqueness of solutions with small unbounded locus. We give applications to Kahler-Einstein metrics with prescribed singularity, and we show that the log-concavity property holds for non-pluripolar products with small unbounded locus.

v2. Improved presentation. Examples added. v.3 final version, with only small modifications

References in corpus (1)

• Quasiplurisubharmonic Green functions

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