Prolongement d'un courant positif plurisousharmonique

Dabbek, Khalifa

doi:10.1016/j.crma.2006.03.017

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Actually, the authors in [10] considered the case when S = 0. The case when dd c T exists and H 2p (A ∩ Supp T ) = 0 done by Dabbek in [7]. Dabbek proved that in this case the residual current is positive and closed by using the same technique in [10] with the local potential of a positive closed current given in [5].…”

Section: Of Course the Condition On The Hausdorff Dimension In Theorementioning

confidence: 99%

Extension of Positive Currents with Special Properties of Monge-Ampère Operators

Abdulaali

2013

MATH. SCAND.

View full text Add to dashboard Cite

In this paper we study the extension of currents across small obstacles. Our main results are: 1) Let $A$ be a closed complete pluripolar subset of an open subset $\Omega$ of $\mathsf{C}^n$ and $T$ be a negative current of bidimension $(p,p)$ on $\Omega\setminus A$ such that $dd^{c}T\geq-S$ on $\Omega\setminus A$ for some positive plurisubharmonic current $S$ on $\Omega$. Assume that the Hausdorff measure $\mathscr{H}_{2p}(A\cap \overline{\operatorname{Supp} T})=0$. Then $\widetilde{T}$ exists. Furthermore, the current $R= \widetilde{dd^{c}T}-{dd}^{c} \widetilde{T}$ is negative supported in $A$. 2) Let $u$ be a positive strictly $k$-convex function on an open subset $\Omega$ of $\mathsf{C}^n$ and set $A=\{z\in\Omega:u(z)=0\}$. Let $T$ be a negative current of bidimension $(p,p)$ on $\Omega\setminus A$ such that $dd^{c}T\geq -S$ on $\Omega\setminus A$ for some positive plurisubharmonic (or $dd^{c}$-negative) current $S$ on $\Omega$. If $p\geq k+1$, then $\widetilde{T}$ exists. If $p\geq k+2$, $dd^{c}S\leq 0$ and $u$ of class $\mathscr{C}^{2}$, then $\widetilde{dd^{c}T}$ exists and $\widetilde{dd^{c}T}= dd^{c}\widetilde{T}$.

show abstract

Section: Of Course the Condition On The Hausdorff Dimension In Theorementioning

confidence: 99%

Extension of Positive Currents with Special Properties of Monge-Ampère Operators

Abdulaali

2013

MATH. SCAND.

View full text Add to dashboard Cite

show abstract

“…Le cas d'un courant positif fermé est démontré par El Mir-Feki [8], le cas d'un courant négatif plurisousharmonique (S = 0) est démontré par Dabbek, Elkhadhra et El Mir [4], alors que le cas d'un courant positif plurisousharmonique (psh) où son dd c est supposé de masse localement finie est démontré par Dabbek [2] (en choisissant S = dd c T ). …”

Section: Cas D'un Obstacle Fermé Pluripolaire Completunclassified

Prolongement d’un courant positif quasi-plurisurharmonique

Ghiloufi¹,

Dabbek²

2009

Ann. math. Blaise Pascal

Self Cite

View full text Add to dashboard Cite

Prolongement d'un courant positif plurisousharmonique

Cited by 2 publications

References 7 publications

Extension of Positive Currents with Special Properties of Monge-Ampère Operators

Extension of Positive Currents with Special Properties of Monge-Ampère Operators

Prolongement d’un courant positif quasi-plurisurharmonique

Contact Info

Product

Resources

About