Convergence in Capacity  [ Convergence en capacité ]
Annales de l'Institut Fourier, Tome 58 (2008) no. 5, p. 1839-1861
Nous étudions la relation entre la convergence en capacité des fonctions pluri sous-harmoniques et la convergence des mesures de Monge-Ampère complexes correspondantes. Nous trouvons un type de convergence des mesures de Monge-Ampère complexe qui est essentiellement équivalent à la convergence en capacité C n des fonctions. Nous montrons aussi que la convergence faible des mesures de Monge-Ampère complexes est équivalente à la convergence en capacité C n-1 des fonctions dans certains cas. Comme application nous donnons des théorèmes de stabilité des solutions des équations de Monge-Ampère.
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.
DOI : https://doi.org/10.5802/aif.2400
Classification:  32W20,  32U15
@article{AIF_2008__58_5_1839_0,
     author = {Xing, Yang},
     title = {Convergence in Capacity},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {5},
     year = {2008},
     pages = {1839-1861},
     doi = {10.5802/aif.2400},
     mrnumber = {2445835},
     zbl = {1152.32021},
     language = {en},
     url = {http://http://www.numdam.org/item/AIF_2008__58_5_1839_0}
}
Xing, Yang. Convergence in Capacity. Annales de l'Institut Fourier, Tome 58 (2008) no. 5, pp. 1839-1861. doi : 10.5802/aif.2400. http://www.numdam.org/item/AIF_2008__58_5_1839_0/

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