On the tangent cones to plurisubharmonic currents

2011/12/15 by Noureddine Ghiloufi, Ghiloufi, Noureddine, Khalifa Dabbek +1
Mathematics · #32U05 #32U25 #32U40 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32U05 #msc:32U25 #msc:32U40

paper · pdf · doi:10.48550/arxiv.1112.3469

18 pages

arxiv created 2011/12/15 · arxiv updated 2011/12/16

Abstract

In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some Estimates of the growth of the Lelong functions associated to the current and to its dd^c are given to ensure the existence of the blow-up of this current. A second proof for the existence of the tangent cone is derived from these estimates.

Related

• Existence of the directional tangent cone to a positive current
• Some achieved wedge products of positive currents
• Tangent cones to positive-(1,1) De Rham currents
• Polynomial hulls and positive currents
• Singularities of plurisubharmonic functions and positive closed currents