Sammanfattning
We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampere measures. We find one type of convergence of complex Monge-Ampbre measures which is essentially equivalent to convergence in the capacity C-n of functions. We also prove that weak convergence of complex Monge-Ampere measures is equivalent to convergence in the capacity Cn-1 of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampere equations.
| Originalspråk | Engelska |
|---|---|
| Sidor (från-till) | 1839-1861 |
| Antal sidor | 24 |
| Tidskrift | Annales de l'Institut Fourier |
| Volym | 58 |
| Nummer | 5 |
| DOI | |
| Status | Publicerad - 2008 |
Nyckelord
- the complex Monge-Ampere operator
- plurisubharmonic function
- capacity
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