The pluricomplex green function with two poles of the unit ball of ℂscript n sign

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Abstract

In this paper we find the formula for the pluricomplex Green function of the unit ball of ℂscript n sign with two poles of equal weights. The strategy will be to show the existence of a foliation of the ball (singular at the poles) by proper smooth analytic discs passing through one or through both of the poles, such that the restriction of the pluricomplex Green function to these discs is harmonic away from the poles. This foliation is obtained by solving a suitable extremal problem, in analogy to the results of Lempert in the case of one pole for convex domains. Using the expression of the Green function along each leaf of the foliation, we construct its formula on the whole ball. We then show that this function is of class C1,1 but not C2.

Original languageEnglish (US)
Pages (from-to)257-283
Number of pages27
JournalPacific Journal of Mathematics
Volume194
Issue number2
DOIs
StatePublished - Jun 2000
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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