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

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (3)
Authors
Khedhiri, Hedi
Contact information
Khedhiri, Hedi: University of Monastir Monastir, Tunisia;
Keywords
closed positive current; plurisubharmonic function; potential; analytic set; Lelong number
Abstract

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)

Pages
331–341
DOI
10.17516/1997-1397-2020-13-3-331-341
Paper at repository of SibFU
http://elib.sfu-kras.ru/handle/2311/135200