Seperable maximal pluriharmonic functions in two complex variables.
Some characterizations of the class and applications
We give some characterizations of the class and use them to establish a lower estimate for the log canonical threshold of plurisubharmonic functions in this class.
Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications
The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge-Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in -capacity then the sequence of the Monge-Ampère measures of subextensions is weakly*-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.
Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.