Pham Hoang Hiep

A comparison principle for the complex Monge-Ampère operator in Cegrell's classes and applications

In this article we will first prove a result about the convergence in capacity. Next we will obtain a general decomposition theorem for complex Monge-Ampere measures which will be used to prove a c ...

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.

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.

ON THE CONVERGENCE IN CAPACITY ON COMPACT KAHLER MANIFOLDS AND ITS APPLICATIONS

The main aim of the present note is to study the convergence inCX,ω on a compact Kahler mainfold X. The obtained results are used to studyglobal extremal functions and describe the ω-pluripolar hul ...