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Non-linearity of the pluricomplex Green function
Author(s):
Frank
Wikström
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1051-1056.
MSC (2000):
Primary 32U35;
Secondary 32F45
Posted:
October 10, 2000
MathSciNet review:
1712869
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Abstract:
We consider the pluricomplex Green function with multiple poles as introduced by Lelong. We give a partial solution to a question concerning the set where the multipole Green function coincides with the sum of the corresponding single pole Green functions.
References:
- 1.
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- 2.
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 , Pacific J. Math. (to appear). - 3.
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- 5.
- A. Edigarian and W. Zwonek, Invariance of the pluricomplex Green function under proper mappings with applications, Complex Variables Theory Appl. 35 (1998), 367-380. MR 99d:32017
- 6.
- M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. France 113 (1985), 231-240. MR 87d:32032
- 7.
- F. Lárusson and R. Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998), 1-39. MR 99e:32020
- 8.
- P. Lelong, Fonction de Green pluricomplexe et lemme de Schwarz dans les espaces de Banach, J. Math. Pures Appl. 68 (1989), 319-347. MR 91c:46065
- 9.
- L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. MR 84d:32036
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Additional Information:
Frank
Wikström
Affiliation:
Department of Mathematics, Umeå University, S-901 87 Umeå, Sweden
Email:
Frank.Wikstrom@math.umu.se
DOI:
10.1090/S0002-9939-00-05683-5
PII:
S 0002-9939(00)05683-5
Keywords:
Pluricomplex Green function with multiple poles,
analytic discs,
invariant distances
Received by editor(s):
June 25, 1999
Posted:
October 10, 2000
Communicated by:
Steven R. Bell
Copyright of article:
Copyright
2000,
American Mathematical Society
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