Convergence in capacity

Xing, Yang

doi:10.5802/aif.2400

Abstract

We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampere measures. We find one type of convergence of complex Monge-Ampbre measures which is essentially equivalent to convergence in the capacity C-n of functions. We also prove that weak convergence of complex Monge-Ampere measures is equivalent to convergence in the capacity Cn-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampere equations.

Keywords

the complex Monge-Ampere operator; plurisubharmonic function; capacity

Published in

Annales de l'Institut Fourier
2008, volume: 58, number: 5, pages: 1839-1861
Publisher: ANNALES INST FOURIER

SLU Authors

Xing, Yang
- Department of Forest Economics, Swedish University of Agricultural Sciences

UKÄ Subject classification

Other Mathematics

Publication identifier

DOI: https://doi.org/10.5802/aif.2400

Permanent link to this page (URI)

https://res.slu.se/id/publ/18940