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Vietnam Journal of Mathematics 35:3(2007) 317-330 |
An Example of Limit of Lempert Functions |
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Pascal J. Thomas |
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Abstract. The Lempert function for a set of poles in a domain of $\mathbb C^n$ at a point $z$ is obtained by taking a certain infimum over all analytic disks going through the poles and the point $z$, 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 $\mathbb C^2$ coalesces to the origin. |
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2000 Mathematics Subject Classification: 32F07, 32F45. |
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Keywords: Pluricomplex Green function, Lempert function, analytic disks, Schwarz lemma. |
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Vietnam Academy of Science and Technology
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