On the tangent cones to plurisubharmonic currents
type: Item
instance of: scholarly article
title: On the tangent cones to plurisubharmonic currents
zbMATH Open document ID: 1351.32053
author: Khalifa Dabbek
author: Noureddine Ghiloufi
author: Jawhar Hbil
published in: Bulletin des Sciences Mathématiques
publication date: 2016-06-09T00:00:00Z
review text: Let \(T\) be a positive plurisubharmonic (\(i\partial\overline\partial T\geq 0\)) or plurisuperharmonic (\(i\partial\overline\partial T\leq 0\)) current on a neighborhood of \(0\) in \({\mathbb C}^n\). One says that \(T\) has a tangent cone at \(0\) if the weak limit of the family of its homothetic currents exists. In this paper, the authors give a sufficient condition on the projective mass of \(T\), guaranteeing the existence of a tangent cone of \(T\). The proof frequently uses the Lelong-Jensen formula. When \(T\) is closed, the authors recover the result given in [\textit{M. Blel} et al., Ark. Mat. 28, No. 2, 231--248 (1990; Zbl 0724.32005)]. Moreover, some estimates on the the growth of the Lelong function associated to a plurisubharmonic or plurisuperbharmonic current, are obtained in order to prove the existence of the strict transform of such currents.
reviewed by: Fredj Elkhadhra
Mathematics Subject Classification ID: 32U25
Mathematics Subject Classification ID: 32U40
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 6590834
zbMATH Keywords: Lelong numbers
zbMATH Keywords: tangent cone
zbMATH Keywords: plurisubharmonic currents
zbMATH Keywords: plurisubharmonic functions
MaRDI profile type: Publication
full work available at URL: j.bulsci.2015.08.002
OpenAlex ID: W2963793946
cites work: Sur l'existence du cône tangent à un courant positif fermé. (About the existence of the tangent cone with positive closed current)
cites work: On the Lelong-Demailly numbers of plurisubharmonic currents
cites work: Existence of tangent cones to plurisubharmonic currents
cites work: Slicing of closed positive currents and the equation of Lelong-Poincaré
DOI: 10.1016/J.BULSCI.2015.08.002
description: scientific article; zbMATH DE number 6590834