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Research article - Peer-reviewed, 2008

Convergence in capacity

Xing, Yang

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

    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