Lelong numbers of potentials associated with positive closed currents and applications

$m$-potential theory and $m$-generalized Lelong numbers associated with $m$-positive supercurrents

“…If T is assumed to be closed, it was proved by[11] that ν T (a) exists for any a. In analogue with the work of Ghiloufi, Zaway and Hawari[9], the next result describe a relation between the Lelong number of a positive closed current and the Lelong number of his local potential. Theorem 3.…”

“…In the mean while, we investigate a variant of important related properties. Also, Due to Ghiloufi, Zaway and Hawari [9], we describe a relation between the Lelong number of a positive closed supercurrent and the Lelong number of his local potential. Section 4 is reserved for the study of the m-generalized Lelong numbers as a measure of the asymptotic behaviour of the supercurrent T ∧ β n−m ∧ (dd # ϕ) m+p−n near the m-polar set {ϕ = −∞}.…”