Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity
By Tam'as Darvas, E. Di Nezza, Chinh H. Lu. Analysis & PDE, 2017
124 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7465553501c78214bd86a14691246766289e2187
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In Applied Mathematics
- Chinh H. Lu
- Tam'as Darvas
- E. Di Nezza
- Chi Li
- Jingrui Cheng
- Xiuxiong Chen
- Robert J. Berman
- Giovanni Molica Bisci
In Geometry and Topology
- Chinh H. Lu
- Tam'as Darvas
- E. Di Nezza
- Chi Li
- Jingrui Cheng
- Xiuxiong Chen
- Robert J. Berman
- B. Berndtsson
Citations in the corpus
- Log-concavity of volume and complex Monge–Ampère equations with prescribed singularity (2018, methodology): “In this case however solutions will not have the same singularity type as φ, they will come from the slightly bigger relative full mass class E(X , θ, φ) introduced in [17].”