Convergence of multipole Green functions
Nguyen DieuPacal Thomas
32U3532U20plurisubharmonic functionsMonge-Ampere operatorpluricomplex Green functions
We continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\mathbb{C}^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the domain, and where some of them might go to the boundary of the domain. We prove that weak convergence will imply convergence in capacity; that it implies convergence uniformly on compacta away from the poles when no poles tend to the boundary; and that the study can be reduced, in a sense, to the case where poles tend to a single point. Furthermore, we prove that the limits of Green functions can be obtained as limits of functions of the type $\max_{1\le i\le3n}(1/p)\log|f_i|$, where the $f_i$ are holomorphic functions.
Indiana University Mathematics Journal
2016
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10.1512/iumj.2016.65.5766
10.1512/iumj.2016.65.5766
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Indiana Univ. Math. J. 65 (2016) 223 - 241
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