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

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Title: Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity
Authors: Darvas, T
Nezza, ED
Lu, CH
Item Type: Working Paper
Abstract: We establish the monotonicity property for the mass of non-pluripolar products on compact K\"ahler manifolds and initiate the study of complex Monge-Amp\`ere equations with arbitrary prescribed singularity. As applications, we prove existence and uniqueness of K\"ahler--Einstein metrics with prescribed singularity, and we also provide the log-concavity property of non-pluripolar products with small unbounded locus.
Issue Date: 31-Dec-2018
URI: http://hdl.handle.net/10044/1/53410
Copyright Statement: © 2017 The Author(s)
Funder's Grant Number: Marie Skłodowska-Curie Action 660940 — KRF-CY (MSCA–IF)
Keywords: math.DG
math.AP
math.CV
Notes: v2. Improved presentation. Examples added
Appears in Collections:Faculty of Natural Sciences



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