## Experimental Mathematics

### Computing the Pluricomplex Green Function with Two Poles

Frank Wikström

#### Abstract

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 $\C2$.

#### Article information

Source
Experiment. Math., Volume 12, Number 3 (2003), 375-384.

Dates
First available in Project Euclid: 15 June 2004

https://projecteuclid.org/euclid.em/1087329239

Mathematical Reviews number (MathSciNet)
MR2034400

Zentralblatt MATH identifier
1078.32021

Subjects
Primary: 32U35: Pluricomplex Green functions
Secondary: 32F45: Invariant metrics and pseudodistances

#### Citation

Wikström, Frank. Computing the Pluricomplex Green Function with Two Poles. Experiment. Math. 12 (2003), no. 3, 375--384. https://projecteuclid.org/euclid.em/1087329239