Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1839-1861 |
| Number of pages | 24 |
| Journal | Annales de l'Institut Fourier |
| Volume | 58 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2008 |
Keywords
- the complex Monge-Ampere operator
- plurisubharmonic function
- capacity
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