We look at numerical computations of the pluricomplex Green function g with two poles of equal weight for the bidisk. The results we obtain strongly suggest that Coman's conjecture holds in this setting, that is that g equals the Lempert function. We also prove this in a special case.
¶ Furthermore, we show that Coman's conjecture fails in the case of two poles of different weight in the unit ball of $\C2$.
Publié le : 2003-05-14
Classification:
Pluricomplex Green function,
Lempert function,
interval arithmetic,
32U35,
32F45
@article{1087329239,
author = {Wikstr\"om, Frank},
title = {Computing the Pluricomplex Green Function with Two Poles},
journal = {Experiment. Math.},
volume = {12},
number = {1},
year = {2003},
pages = { 375-384},
language = {en},
url = {http://dml.mathdoc.fr/item/1087329239}
}
Wikström, Frank. Computing the Pluricomplex Green Function with Two Poles. Experiment. Math., Tome 12 (2003) no. 1, pp. 375-384. http://gdmltest.u-ga.fr/item/1087329239/