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

Abstract

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.

Keywords:

• Monge–Ampère operator
• subextension
• approximation
• plurisubharmonic functions

AMS Subject Classifications:

• 32U05
• 32W20

Acknowledgements

The author would like to thank the referees for valuable remarks which lead to the improvements of the exposition of the paper.