Computing the Pluricomplex Green Function with Two Poles

Abstract

We look at numerical computations of the pluricomplex Green function g with two poles of equal weight for the bidisk. The resultswe obtain strongly suggest that Coman's conjecture holds in this setting, that is that g equals the Lempertfunction. 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 .

Keywords:

• Pluricomplex Green function
• Lempert function
• interval arithmetic