scholarly journals On the measures of large entropy on a positive closed current

2015 ◽  
Vol 280 (3-4) ◽  
pp. 919-944 ◽  
Author(s):  
Henry de Thélin ◽  
Gabriel Vigny
Keyword(s):  
Closed Current ◽  
Positive Closed Current

scholarly journals On Construction of Positive Closed Currents with Prescribed Lelong Numbers

2020 ◽  
pp. 331-341
Author(s):  
Hedi Khedhiri
Keyword(s):  
Growth Condition ◽  
Compact Subset ◽  
Level Set ◽  
Level Sets ◽  
Plurisubharmonic Function ◽  
Lelong Numbers ◽  
The Family ◽  
Closed Current ◽  
Upper Level ◽  
Positive Closed Current

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)

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

2017 ◽  
Vol 28 (14) ◽  
pp. 1750110 ◽  
Author(s):  
James J. Heffers
Keyword(s):  
Projective Space ◽  
Level Set ◽  
Level Sets ◽  
Complex Projective Space ◽  
Lelong Number ◽  
Lelong Numbers ◽  
Closed Current ◽  
Upper Level ◽  
Complex Projective ◽  
Positive Closed Current

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.

scholarly journals DESINGULARIZATION OF QUASIPLURISUBHARMONIC FUNCTIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 555-560 ◽  
Author(s):  
VINCENT GUEDJ
Keyword(s):  
Complex Surface ◽  
Lelong Numbers ◽  
Compact Complex Surface ◽  
Closed Current ◽  
Positive Closed Current

Let T be a positive closed current of bidegree (1,1) on a compact complex surface. We show that for all ε > 0, one can find a finite composition of blow-ups π such that π*T decomposes as the sum of a divisorial part and a positive closed current whose Lelong numbers are all less than ε.

scholarly journals Modes of Energy Loss from Isolated Magnetized Neutron Star

1987 ◽  
Vol 125 ◽  
pp. 450-450
Author(s):  
S. Shibata
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Gamma Ray ◽  
Rotational Energy ◽  
Pair Creation ◽  
Dipole Radiation ◽  
Pair Plasma ◽  
Electron Positron ◽  
Closed Current ◽  
Electron Positron Pair

Pulsar may be regarded as a discharge tube by electron-positron pair creation. On this viewpoint we carry out two numerical calculations. The obtained magnetic field is consistent with the flow. We find that pulsars emit their rotational energy through three modes simultaneously. The three modes are (1)relativistic acceleration and following gamma-ray emission in the closed current circuit in the magnetosphere, (2)wind of the electron-positron pair plasma, and (3)dipole radiation.

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