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Nguyen Quang Dieu and Pascal Thomas, Convergence of multipole Green functions, Indiana University Mathematical Journal, Vol 65, 223-241, 2016
02/10/2017 02:38:10


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 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 $max_{1le ile 3n} frac{1}{p} log |f_i|$, where the $f_i$ are holomorphic functions.

Link: https://www.researchgate.net/publication/263620028_Convergence_of_Multipole_Green_Functions

· Nguyen Quang Dieu and Pascal Thomas, Convergence of multipole Green functions, Indiana University Mathematical Journal, Vol 65, 223-241, 2016
· Nguyen Xuan Hong, Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions, C. R. Acad. Sci. Paris, Ser. I, 355 (2017), 487-492
· Nguyen Xuan Hong, Nguyen Van Trao and Tran Van Thuy, Convergence in capacity of plurisubharmonic functions with given boundary values, International Journal of Mathematics, Vol. 28, No. 3 (2017) 1750018 (14 pages)
· Nguyen Van Trao, Hoang Viet and Nguyen Xuan Hong, Approximation of plurifinely plurisubharmonic functions, Journal of Mathematical Analysis and Applications, 450 (2017), 1062-1075
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· Le Mau Hai and Pham Hoang Hiep, An equality on the complex Monge-Ampere measures. J. Math. Anal. Appl., 444(2016), 503-511.
· Le Mau Hai, Tang Van Long and Trieu Van Dung, Equations of complex Monge–Amp`ere type for arbitrary measures and applications, Inter. J. Math, Vol 27, No 4 ( 2016), 1650035 ( 13 pages).
· Le Mau Hai, Thai Thuan Quang, Duong Thanh Vy and Le Thanh Hung, Some Classes of Banach Analytic Spaces, Math. Proceed. Royal Irish Academy, Vol 116A, No1 (2016), 1-17
· Le Mau Hai, Nguyen Van Khiem and Trieu Van Dung, Subextension of plurisubharmonic functions in unbounded hyperconvex domains and applications, Complex Var. Elliptic Equ., Vol 61, (2016), No.8, 1116-1132.
· Phung Van Manh, On the smoothness of certain composite functions, Analysis mathematica, 43 (2017), 501-510.
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