Green vs. Lempert functions: a minimal example
arXiv:1104.1985
Abstract
The Lempert function for a set of poles in a domain of at a point is obtained by taking a certain infimum over all analytic disks going through the poles and the point , and majorizes the corresponding multi-pole pluricomplex Green function. Coman proved that both coincide in the case of sets of two poles in the unit ball. We give an example of a set of three poles in the unit ball where this equality fails.
v3: proof of the upper estimate for the Green function added; accepted in Pacific Journal of Mathematics