GREEN VERSUS LEMPERT FUNCTIONS: A MINIMAL EXAMPLE

The Lempert function for a set of poles in a domain of C-n at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z; it majorizes the corresponding multipole 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.