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Vietnam Journal of Mathematics 35:3(2007) 317-330

 An Example of Limit of Lempert Functions

Pascal J. Thomas

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. We investigate the precise behavior of the Lempert function as a set of three poles in C² coalesces to the origin.

2000 Mathematics Subject Classification: 32F07, 32F45.

Keywords: Pluricomplex Green function, Lempert function, analytic disks, Schwarz lemma.

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Published by Springer since January 2013