Monotonicity of non-pluripolar products and complex Monge-Amp\`ere equations with prescribed singularity
Differential Geometry
2018-06-13 v3 Analysis of PDEs
Complex Variables
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.
Keywords
Cite
@article{arxiv.1705.05796,
title = {Monotonicity of non-pluripolar products and complex Monge-Amp\`ere equations with prescribed singularity},
author = {Tamás Darvas and Eleonora Di Nezza and Chinh H. Lu},
journal= {arXiv preprint arXiv:1705.05796},
year = {2018}
}
Comments
v2. Improved presentation. Examples added. v.3 final version, with only small modifications