Convergence in Capacity
Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1839-1861.

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.

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.

DOI: 10.5802/aif.2400
Classification: 32W20, 32U15
Keywords: the complex Monge-Ampère operator, plurisubharmonic function, capacity

Xing, Yang 1

1 Swedish University of Agricultural Sciences Centre of Biostochastics 901 83 Umeå(Sweden)
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Xing, Yang. Convergence in Capacity. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1839-1861. doi : 10.5802/aif.2400. https://aif.centre-mersenne.org/articles/10.5802/aif.2400/

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