Weak convergence of currents

Summary, in English

We give certain condictions to guarantee weak convergence $u_kT_k \rightarrow uT$, where $u_k$, $u$ are plurisubharmonic functions and $T_k$, $T$ are positive closed currents. As applications we obtain that convergence in capacity of plurisubharmonic functions $u_k$ implies weak convergence of the complex Monge-Amp\`ere measures $(dd^cu_k)^n$ if all of the plurisubharmonic functions $u_k$ are bounded below by one of some sorts of plurisubharmonic functions.

• Författare: Yang Xing
• Publiceringsår: 2008
• Språk: Engelska
• Sidor: 253-264
• Publikation/Tidskrift/Serie: Mathematische Zeitschrift
• Volym: 260
• Issue: 2
• Länkar: http://dx.doi.org/10.1007/s00209-007-0271-8
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0025-5874