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 of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity 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 des fonctions. Nous montrons aussi que la convergence faible des mesures de Monge-Ampère complexes est équivalente à la convergence en capacité des fonctions dans certains cas. Comme application nous donnons des théorèmes de stabilité des solutions des équations de Monge-Ampère.
Keywords: the complex Monge-Ampère operator, plurisubharmonic function, capacity
Xing, Yang 1
@article{AIF_2008__58_5_1839_0, author = {Xing, Yang}, title = {Convergence in {Capacity}}, journal = {Annales de l'Institut Fourier}, pages = {1839--1861}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {5}, year = {2008}, doi = {10.5802/aif.2400}, mrnumber = {2445835}, zbl = {1152.32021}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2400/} }
TY - JOUR AU - Xing, Yang TI - Convergence in Capacity JO - Annales de l'Institut Fourier PY - 2008 SP - 1839 EP - 1861 VL - 58 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2400/ DO - 10.5802/aif.2400 LA - en ID - AIF_2008__58_5_1839_0 ER -
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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