Existence of tangent cones to plurisubharmonic currents

Haggui, Fathi

doi:10.1080/17476933.2010.551205

Cited by 4 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This theorem is due to Blel-Demailly-Mouzali in case of positive closed currents. In [6], Haggui proved the same result for T ∈ P + p (Ω). His proof is based on the potential current associated to dd c T .…”

Section: Proof Of the Main Resultsmentioning

confidence: 56%

On the tangent cones to plurisubharmonic currents

Ghiloufi¹,

Dabbek²

2011

Preprint

View full text Add to dashboard Cite

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.Sur les cônes tangents au courants plurisousharmoniques. Résumé. Dans cet article, nous étudions l'existence du cône tangent à un courant positif plurisousharmonique ou plurisurharmonique avec une condition convenable. Des estimations de croissance des fonctions de Lelong associées au courant et à son dd c sont données pour assurer l'existence du relèvement de ce courant. Une deuxième preuve de l'existence du cône tangent se déduit de ces estimations.

show abstract

Section: Proof Of the Main Resultsmentioning

confidence: 56%

On the tangent cones to plurisubharmonic currents

Ghiloufi¹,

Dabbek²

2011

Preprint

View full text Add to dashboard Cite

show abstract

“…In [4], Haggui proved the same result for T ∈ P + p (Ω) using the Lelong-Skoda potential associated with dd c T .…”

Section: Proof Of the Main Resultsmentioning

confidence: 57%

On the tangent cones to plurisubharmonic currents

Dabbek

Ghiloufi

Hbil

2016

Bulletin des Sciences Mathématiques

View full text Add to dashboard Cite

“…Based on the construction of Kiselman which use essentially the projective mass of the current, Blel, Demailly and Mouzali [2] have given two independent conditions where each one ensure the existence of the tangent cone to a positive closed current. Recently, Haggui [7] has shown that one of these conditions remains sufficient even for the case of positive plurisubharmonic currents. This result has been found and generalized by Ghiloufi and Dabbek [4] in the case of a positive plurisubharmonic (psh) or plurisuperharmonic (prh) current.…”

Section: Introductionmentioning

confidence: 99%

Existence of the directional tangent cone to a positive current

Hawari

Hbil

Ghiloufi

2013

Complex Variables and Elliptic Equations

View full text Add to dashboard Cite

In this paper, we start by proving the existence of the strict transform of a positive current T as soon as its jth currents, T j , are plurisubharmonic or plurisuperharmonic. Then, under a suitable condition on T j , we show the existence of the directional tangent cone to T . In the particular case, when T is closed, we give a second condition independent to the previous one.Existence du cône tangent directionnel à un courant positif. Résum é. Dans la première partie de cet article, on montre l'existence du relève-ment d'un courant positif T , par un éclatement de centre lisse, dès que ses jè me courants T j soient plurisousharmoniques ou plurisurharmoniques. Ensuite, avec une condition supplémentaire sur les courants T j , on prouve l'existence du cône tangent directionnel à T . Dans le cas particulier où T est fermé, une deuxième condition indépendante de la première sera donnée.

show abstract

Existence of tangent cones to plurisubharmonic currents

Cited by 4 publications

References 7 publications

On the tangent cones to plurisubharmonic currents

On the tangent cones to plurisubharmonic currents

On the tangent cones to plurisubharmonic currents

Existence of the directional tangent cone to a positive current

Contact Info

Product

Resources

About