On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds

2024/04/04 by Yinji Li, Zhiwei Wang, Li, Yinji +3
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2404.03246

openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,ω) be a compact Hermitian manifold of complex dimension n. Let β be a smooth real closed (1,1) form such that there exists a function ρ∈ PSH(X,β)∩ L^∞(X). We study the range of the complex non-pluripolar Monge-Ampère operator ⟨(β+dd^c⋅)ⁿ⟩ on weighted Monge-Ampère energy classes on X. In particular, when ρ is assumed to be continuous, we give a complete characterization of the range of the complex Monge-Ampère operator on the class \mathcal E(X,β), which is the class of all φ∈ PSH(X,β) with full Monge-Ampère mass, i.e. ∫_X⟨ (β+dd^cφ)ⁿ⟩=∫_Xβⁿ.

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