Relative non-pluripolar product of currents on compact Hermitian manifolds

2025/05/30 by Zhenghao Li, Li, Zhenghao, Shuang Su +1
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2505.24702

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On a class of compact Hermitian manifolds including compact Kähler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms of masses on such manifolds.

Citations

• Volumes of components of Lelong upper level sets II
• Volume of components of Lelong upper-level sets
• The volume of pseudoeffective line bundles and partial equilibrium
• Monotonicity of non-pluripolar Monge-Ampère masses
• Monge-Ampère equations in big cohomology classes
• Super-potentials for currents on compact Kaehler manifolds and dynamics of automorphisms
• Super-potentials of positive closed currents, intersection theory and dynamics

Related

• Relative non-pluripolar products of currents
• Density currents and relative non-pluripolar products
• Loss of mass of non-pluripolar products
• Plurisupported Currents on Compact Kähler Manifolds
• Integration by parts formula for non-pluripolar product