Convergence in capacity of plurisubharmonic functions with given boundary values

DOI10.1142/S0129167X17500185zbMath1368.32026arXiv1601.03152OpenAlexW2963686133MaRDI QIDQ2988751

Tran van Thuy, Nguyen Xuan Hong, Nguyen Van Trao

Publication date: 19 May 2017

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.03152

zbMATH Keywords

plurisubharmonic functionsconvergence in capacitycomplex Monge-Ampère operator

Mathematics Subject Classification ID

Complex Monge-Ampère operators (32W20)

Related Items

Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions ⋮ Capacity and stability on some Cegrell classes of \(m\)-subharmonic functions ⋮ Local maximality for bounded plurifinely plurisubharmonic functions ⋮ A note on maximal subextensions of plurisubharmonic functions ⋮ Complex Monge-Ampère equations for plurifinely plurisubharmonic functions ⋮ Range of the complex Monge–Ampère operator on plurifinely domain ⋮ The stability of solutions to the complex Monge-Ampère equations in bounded \(\mathcal{F} \)-hyperconvex domains ⋮ Weak solutions to the complex \(m\)-Hessian equation on open subsets of \(\mathbb{C}^n\) ⋮ Hölder continuous solutions to the complex Monge-Ampère equations in non-smooth pseudoconvex domains ⋮ The Dirichlet problem for the complex Monge-Ampère operator on strictly plurifinely pseudoconvex domains ⋮ Weak solutions to the complex Monge-Ampère equation on open subsets of \(\mathbb{C}^n\)

Cites Work

• Unnamed Item
• A new capacity for plurisubharmonic functions
• Convergence in capacity
• Monge-Ampère measures on pluripolar sets
• The Dirichlet problem for a complex Monge-Ampère equation
• Pluricomplex energy
• The general definition of the complex Monge-Ampère operator.
• On the \(L^ p\) stability for the complex Monge-Ampère operator
• The locally \(\mathcal{F}\)-approximation property of bounded hyperconvex domains
• Stability of solutions to complex Monge-Ampère equations in big cohomology classes
• The equation of complex Monge-Ampère type and stability of solutions
• The Monge–Ampère type equation in the weighted pluricomplex energy class
• Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications
• Convergence in Capacity
• The complex Monge–Ampère equation in unbounded hyperconvex domains in ℂⁿ
• A comparison principle for the complex Monge-Ampère operator in Cegrell’s classes and applications
• Subextension of plurisubharmonic functions with boundary values in weighted pluricomplex energy classes
• A general Dirichlet problem for the complex Monge–Ampère operator
• Continuity of the complex Monge-Ampère operator
• Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values
• The complex Monge-Ampère equation and pluripotential theory
• Convergence in capacity and applications