Green vs. Lempert functions: a minimal example
Abstract
The Lempert function for a set of poles in a domain of Cn at a point z is obtained by taking a certain infimum over all analytic disks going through the poles and the point z, 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.
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