The complex Monge–Ampère equation in unbounded hyperconvex domains in ℂn

DOI10.1080/17476933.2013.879385zbMath1305.32019OpenAlexW2039506298MaRDI QIDQ2929338

Nguyen Van Trao, Nguyen Xuan Hong, Le Mau Hai

Publication date: 11 November 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2013.879385

zbMATH Keywords

plurisubharmonic functionscomplex Monge-Ampère equationmaximal plurisubharmonic functionunbounded hyperconvex domains

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05) Plurisubharmonic exhaustion functions (32U10)

Related Items (12)

Subextension of plurisubharmonic functions with boundary values in weighted pluricomplex energy classes ⋮ Approximation of plurifinely plurisubharmonic functions ⋮ Capacity and stability on some Cegrell classes of \(m\)-subharmonic functions ⋮ Complex Monge-Ampère equations for plurifinely plurisubharmonic functions ⋮ Range of the complex Monge–Ampère operator on plurifinely domain ⋮ Convergence in capacity of plurisubharmonic functions with given boundary values ⋮ Subextension of plurisubharmonic functions in unbounded hyperconvex domains and applications ⋮ Weak solutions to the complex \(m\)-Hessian equation on open subsets of \(\mathbb{C}^n\) ⋮ Weakly solutions to the complex Monge-Ampère equation on bounded plurifinely hyperconvex domains ⋮ Weak solutions to the complex Monge-Ampère equation on open subsets of \(\mathbb{C}^n\) ⋮ Envelope of plurisubharmonic functions in Cegrell's classes ⋮ Weak solutions to the complex \(m\)-Hessian type equations for arbitrary nonnegative Radon measures on open subsets of \(\mathbb{C}^n\)

Cites Work

• The Bremermann-Dirichlet problem for unbounded domains of \({\mathbb{C}}^n\)
• Monge-Ampère measures on pluripolar sets
• The Dirichlet problem for the complex Monge-Ampère operator: Stability in \(L^ 2\)
• The Dirichlet problem for a complex Monge-Ampère equation
• Pluricomplex energy
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• The general definition of the complex Monge-Ampère operator.
• Local property of the class \(\mathcal E_{\chi}, loc\)
• The complex Monge–Ampère equation for complex homogeneous functions in Cⁿ
• Convergence in Capacity
• A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
• A general Dirichlet problem for the complex Monge–Ampère operator
• Subextension of plurisubharmonic functions without increasing the total Monge–Ampère mass
• Approximation of Plurisubharmonic Functions and the Dirichlet Problem for the Complex Monge-Ampère Operator.
• The range of the complex Monge-Ampere operator II

This page was built for publication: The complex Monge–Ampère equation in unbounded hyperconvex domains in ℂⁿ