Computing the Pluricomplex Green Function with Two Poles

Abstract

CONTENTS 1. Introduction 2. Computing δ 3. Computing δ * 4. Numerical Computation of δ 5. Numerical Computation of δ * 6. Results of the Numerical Computation 7. A Counterexample to Coman's Conjecture Acknowledgments References

Coman conjecture for the bidisc

“…Recall that a partial positive answer in this case was found in [5] (see also [8]) in the case the poles were lying on D × {0}. In [20] numerical computations were carried out which strongly suggested that the equality in the case D = D 2 , N = 2, ν 1 = ν 2 should hold. The aim of this paper is to show that actually the Coman conjecture holds in the bidisk (D = D 2 ), N = 2, two arbitrary poles and ν 1 = ν 2 .…”