An existence theorem for non-pluripolar complex Monge-Ampère type equations on hyperconvex domains

2025/07/24 by Thai Duong, Do, Thai Duong, Ngoc Thanh Cong Pham +1
Mathematics · #31C10 #32U15 #32U40 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.18116

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the non-pluripolar complex Monge-Ampère measure on bounded domains in \( ℂⁿ \). We establish a general existence theorem for a non-pluripolar complex Monge-Ampère type equation with prescribed singularity on a bounded hyperconvex domain in \( ℂⁿ \).

Citations

• A Dirichlet type problem for non-pluripolar complex Monge-Ampère equations
• Some remarks on the Cegrell's class F
• Complex Monge-Ampère equation in strictly pseudoconvex domains
• Monge-Ampère equations in big cohomology classes
• Weighted pluricomplex energy
• Plurisubharmonic functions with weak singularities
• Monge-Ampere measures on pluripolar sets
• The weigthed Monge-Ampère energy of quasiplurisubharmonic functions
• Convergence in capacity

Related

• A Dirichlet type problem for non-pluripolar complex Monge-Ampère equations
• Weakly solutions to the complex Monge-Amp `ere equation on bounded\n plurifinely hyperconvex domains
• Complex Monge-Ampère equations for plurifinely plurisubharmonic functions
• Complex Monge-Ampère equation in strictly pseudoconvex domains
• Degenerate complex Monge-Ampère equations with non-Kähler forms in bounded domains