TY - JOUR

T1 - The pluricomplex green function with two poles of the unit ball of ℂscript n sign

AU - Coman, Dan

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2000/6

Y1 - 2000/6

N2 - 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.

AB - 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.

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U2 - 10.2140/pjm.2000.194.257

DO - 10.2140/pjm.2000.194.257

M3 - Article

AN - SCOPUS:0039411832

VL - 194

SP - 257

EP - 283

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -