THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY
2000 ◽
Vol 11
(04)
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pp. 509-522
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Keyword(s):
In this article we deal with the behavior of the pluricomplex Green function GD(·;w), of a pseudoconvex domain D in [Formula: see text], when the pole tends to a boundary point. In [7], it was shown that, given a boundary point w0 of a hyperconvex domain D, then there is a pluripolar set E⊂D, such that lim sup w→w0 GD(z;w)=0 for z∈D\E. Under an additional assumption on D, that can be viewed as natural, one can avoid the pluripolar exceptional set. Our main result is that on a bounded domain [Formula: see text] that admits a Hoelder continuous plurisubharmonic exhaustion function ρ:D→[-1,0), the pluricomplex Green function GD(·,w) tends to zero uniformly on compact subsets of D, if the pole w tends to a boundary point w0 of D.
2012 ◽
Vol 23
(06)
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pp. 1250065
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2003 ◽
Vol 171
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pp. 107-125
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2000 ◽
Vol 129
(4)
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pp. 1051-1056
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1973 ◽
Vol 79
(4)
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pp. 749-752
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2009 ◽
Vol 91
(4)
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pp. 364-383
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Keyword(s):
1993 ◽
Vol 72
(2)
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pp. 487-502
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2019 ◽
Vol 23
(13)
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pp. 221-250
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