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Convergence in capacity

Xing, Yang LU (2008) In Annales de l'Institut Fourier 58(5). p.1839-1861
Abstract
We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Annales de l'Institut Fourier
volume
58
issue
5
pages
1839 - 1861
publisher
ANNALES DE L INSTITUT FOURIER
ISSN
0373-0956
language
English
LU publication?
no
id
418c399e-797e-4f32-a2ca-cfa3b7c7ea15 (old id 1465059)
alternative location
http://aif.cedram.org/cedram-bin/article/AIF_2008__58_5_1839_0.pdf
date added to LUP
2009-08-20 13:46:33
date last changed
2016-06-29 09:01:41
@article{418c399e-797e-4f32-a2ca-cfa3b7c7ea15,
  abstract     = {We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.},
  author       = {Xing, Yang},
  issn         = {0373-0956},
  language     = {eng},
  number       = {5},
  pages        = {1839--1861},
  publisher    = {ANNALES DE L INSTITUT FOURIER},
  series       = {Annales de l'Institut Fourier},
  title        = {Convergence in capacity},
  volume       = {58},
  year         = {2008},
}