On Construction of Positive Closed Currents with Prescribed Lelong Numbers

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)

A Property of upper level sets of Lelong numbers of currents on ℙ2

Let [Formula: see text] be a positive closed current of bidimension [Formula: see text] with unit mass on the complex projective space [Formula: see text]. For [Formula: see text] and [Formula: see text] we show that if [Formula: see text] has four points with Lelong number at least [Formula: see text], the upper level set [Formula: see text] of points of [Formula: see text] with Lelong number strictly larger than [Formula: see text] is contained within a conic with the exception of at most one point.

A physical explanation for the magnetic decrease ahead of dipolarization fronts

Recent studies have shown that the ambient plasma in the near-Earth magnetotail can be compressed by the arrival of a dipolarization front (DF). In this paper we study the variations in the characteristics of currents flowing in this compressed region ahead of the DF, particularly the changes in the cross-tail current, using observations from the THEMIS satellites. Since we do not know whether the changes in the cross-tail current lead to a field-aligned current formation or just form a current loop in the magnetosphere, we thus use redistribution to represent these changes of local current density. We found that (1) the redistribution of the cross-tail current is a common feature preceding DFs; (2) the redistribution of cross-tail current is caused by plasma pressure gradient ahead of the DF and (3) the resultant net current redistributed by a DF is an order of magnitude smaller than the typical total current associated with a moderate substorm current wedge (SCW). Moreover, our results also suggest that the redistributed current ahead of the DF is closed by currents on the DF itself, forming a closed current loop around peaks in plasma pressure, what is traditionally referred to as a banana current.