Convergence in capacity
(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:
https://lup.lub.lu.se/record/1465059
- author
- Xing, Yang LU
- publishing date
- 2008
- 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
- external identifiers
-
- scopus:50849116084
- 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
- 2016-04-01 12:02:50
- date last changed
- 2022-01-26 22:01:51
@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}},
url = {{http://aif.cedram.org/cedram-bin/article/AIF_2008__58_5_1839_0.pdf}},
volume = {{58}},
year = {{2008}},
}