Nguyen Xuan Hong

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

In this paper, we look for solutions of the complex Monge–Ampère equation with boundary values in an unbounded hyperconvex domain of .

Range of the complex Monge–Ampère operator on plurifinely domain

Abstract In this paper, we study the Dirichlet problem in a plurifinely domain of . We prove that under the suitable conditions, the complex Monge–Ampère equation can be solved in .

Convergence in capacity of plurisubharmonic functions with given boundary values

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge-Amp\`ere equations.

Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values

The aim of the paper is to investigate the Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values. As an application, we study the approximation of negative plurisubharmonic function with given boundary values by an increasing sequence of plurisubharmonic functions defined in larger domains.

Subextension of plurisubharmonic functions with boundary values in weighted pluricomplex energy classes

In this paper, we investigate subextension of plurisubharmonic functions in the weighted pluricomplex energy class . Moreover, we show the equality of the weighted Monge–Ampère measures of subextension and the given function.

Hölder continuous solutions to the complex Monge–Ampère equations in non-smooth pseudoconvex domains

In this paper, we prove the Hölder continuity for solutions to the complex Monge–Ampère equations on non-smooth pseudoconvex domains of plurisubharmonic type m.

q-subharmonicity and q-convex domains in ℂn

In this paper we study q-subharmonic and q-plurisubharmonic functions in ℂn. Next as an application, we give the notion of q-convex domains in ℂn which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.

Weakly Solutions to the Complex Monge–Ampère Equation on Bounded Plurifinely Hyperconvex Domains

Let

Approximation of plurifinely plurisubharmonic functions

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