Le Mau Hai

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 .

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.

The Monge–Ampère type equation in the weighted pluricomplex energy class

In the paper, we prove the existence of solutions of the complex Monge–Ampere type equation -χ(u)(ddcu)n = μ in the class if there exist subsolutions in this class. As an application, we prove that the complex Monge–Ampere equation (ddcu)n = μ is solvable in the class if there exist subsolutions locally. Moreover, by an example we show that the conditions in our above result are sharp.

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.

THE LOG CANONICAL THRESHOLD OF HOLOMORPHIC FUNCTIONS

In this paper we give the relation between the log canonical threshold c0(f) and the geometry of the zero set {f = 0} of a holomorphic function f. Applying the above relation we give a simple proof for the ascending chain condition in dimension two.

Equations of complex Monge–Ampère type for arbitrary measures and applications

In this paper, we prove the existence of weak solutions of equations of complex Monge–Ampere type for arbitrary measures, in particular, measures carried by pluripolar sets. As an application of the obtained result, we show the existence of weak solutions of equations of complex Monge–Ampere type in the class 𝒩(Ω,f) if there exist locally subsolutions.

Subextension of plurisubharmonic functions in unbounded hyperconvex domains and applications

The aim of the paper was to investigate subextension of plurisubharmonic functions in unbounded hyperconvex domains without changing the Monge–Ampère measures. As an application, we study approximation of plurisubharmonic functions with given boundary values in unbounded hyperconvex domains in .

The Complex Monge–Ampère Operator on Bounded Domains in {\mathbb{C}^{n}}

Abstract.The aim of the present paper is to establish the inequality of Xing’s type for the class

The Linear invariants (DN) and ([omega]) for spaces of germs of holomorphic functions on compact subsets of Cn

{\mathcal{D}}