Journal of Siberian Federal University. Mathematics & Physics / On Construction of Positive Closed Currents with Prescribed Lelong Numbers

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Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (3)
Khedhiri, Hedi
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Khedhiri, Hedi: University of Monastir Monastir, Tunisia;
closed positive current; plurisubharmonic function; potential; analytic set; Lelong number

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)

Paper at repository of SibFU