Weak convergence of currents

被引：0
作者：
Yang Xing
机构：
[1] University of Umeå,Department of Mathematics
来源：
Mathematische Zeitschrift | 2008年 / 260卷
关键词：
Weak Convergence; Approximation Theorem; Plurisubharmonic Function; Positive Current; Lelong Number;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give certain conditions to guarantee weak convergence ukTk → uT, where uk, u are plurisubharmonic functions and Tk, T are positive closed currents. As applications we obtain that convergence in capacity of plurisubharmonic functions uk implies weak convergence of the complex Monge-Ampère measures (ddcuk)n if all of the plurisubharmonic functions uk are bounded below by one of some sorts of plurisubharmonic functions.
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页码：253 / 264
页数：11
相关论文
共 15 条
  • [1] Azarin V.S.(1980)On the asymptotic behaviour of subharmonic functions of finite order Math. USSR Sb. 36 135-154
  • [2] Bedford E.(1987)Fine topology, Šilov boundary and ( J. Funct. Anal. 72 225-251
  • [3] Taylor B.A.(1982)) Acta Math. 149 1-40
  • [4] Bedford E.(1976)A new capacity for plurisubharmonic functions Invent. Math. 37 1-44
  • [5] Taylor B.A.(1983)The Dirichlet problem for the complex Monge-Ampère operator C. R. Acad. Sci. Paris Ser. I Math. 296 869-871
  • [6] Bedford E.(2006)Discontinuité de l’opérateur de Monge-Ampère complexe Ann. Inst. Fourier 56 423-457
  • [7] Taylor B.A.(1995)Geometry of currents, intersection theory and dynamics of horizontal-like maps Math. Ann. 301 399-419
  • [8] Cegrell U.(2000)Oka’s inequality for currents and applications Can. J. Math. 52 1085-1100
  • [9] Dinh T.C.(1999)Complex Monge-Ampère measures of plurisubharmonic functions with bounded values near the boundary Indiana Univ. Math. J 48 749-765
  • [10] Sibony N.(1996)The complex Monge-Ampère equations with a countable number of singular points Proc. Am. Math. Soc. 124 457-467
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