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Green versus Lempert
functions: A minimal example
Pascal Thomas |
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Vol. 257 (2012), No. 1, 189–197
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Abstract |
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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; 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
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Mathematical Subject Classification 2010
Primary: 32U35, 32F45
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Milestones
Received: 20 June 2011
Revised: 18 October 2011
Accepted: 24 October 2011
Published: 19 June 2012
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Authors |
| Pascal Thomas | |
| Institut de Mathématiques de
Toulouse Université de Toulouse UPS, INSA, UT1, UTM 31062 Toulouse France |
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| http://www.math.univ-toulouse.fr/~thomas | |
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