Vol. 257, No. 1, 2012

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Green versus Lempert functions: A minimal example

Pascal Thomas

Vol. 257 (2012), No. 1, 189–197
Abstract

The Lempert function for a set of poles in a domain of 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.

Keywords
pluricomplex Green function, Lempert function, analytic disks, Schwarz Lemma
Mathematical Subject Classification 2010
Primary: 32U35, 32F45
Milestones
Received: 20 June 2011
Revised: 18 October 2011
Accepted: 24 October 2011
Published: 19 June 2012
Authors
Pascal Thomas
Institut de Mathématiques de Toulouse
Université de Toulouse
UPS, INSA, UT1, UTM
31062 Toulouse
France
http://www.math.univ-toulouse.fr/~thomas