On Construction of Positive Closed Currents with Prescribed Lelong Numbers
2020 ◽
pp. 331-341
Keyword(s):
We establish that a sequence (Xk)k∈N of analytic subsets of a domain Ω in Cn, purely dimensioned, can be released as the family of upper-level sets for the Lelong numbers of some positive closed current. This holds whenever the sequence (Xk)k∈N satisfies, for any compact subset L of Ω, the growth condition Σ k∈N Ck mes(Xk ∩ L) < ∞. More precisely, we built a positive closed current Θ of bidimension (p, p) on Ω, such that the generic Lelong number mXk of Θ along each Xk satisfies mXk = Ck. In particular, we prove the existence of a plurisubharmonic function v on Ω such that, each Xk is contained in the upper-level set ECk (ddcv)
2017 ◽
Vol 28
(14)
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pp. 1750110
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Keyword(s):
2014 ◽
Vol 361
(3-4)
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pp. 981-994
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2005 ◽
Vol 16
(05)
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pp. 555-560
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Keyword(s):
2021 ◽
2006 ◽
Vol 13
(4)
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pp. 379-390
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2002 ◽
Vol 53
(11)
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pp. 2569-2586
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Keyword(s):
Keyword(s):