A Liouville theorem for plurisubharmonic currents

Fredj Elkhadhra[1]; Souad Mimouni[1]

  • [1] Département de Mathématique, Faculté des sciences de Monastir, 5000 Monastir Tunisie.

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

  • Volume: 19, Issue: 3-4, page 651-674
  • ISSN: 0240-2963

Abstract

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The goal of this paper is to extend the concepts of algebraic and Liouville currents, previously defined for positive closed currents by M. Blel, S. Mimouni and G. Raby, to psh currents on ℂ n . Thus, we study the growth of the projective mass of positive currents on ℂ n whose support is contained in a tubular neighborhood of an algebraic subvariety. We also give a sufficient condition guaranteeing that a negative psh current is Liouville. Moreover, we prove that every negative psh algebraic current is Liouville. For the particular case of closed currents, under adequate support conditions, we obtain a structure theorem.

How to cite

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Elkhadhra, Fredj, and Mimouni, Souad. "A Liouville theorem for plurisubharmonic currents." Annales de la faculté des sciences de Toulouse Mathématiques 19.3-4 (2010): 651-674. <http://eudml.org/doc/115872>.

@article{Elkhadhra2010,
abstract = {The goal of this paper is to extend the concepts of algebraic and Liouville currents, previously defined for positive closed currents by M. Blel, S. Mimouni and G. Raby, to psh currents on $\{\mathbb\{C\}\}^n$. Thus, we study the growth of the projective mass of positive currents on $\{\mathbb\{C\}\}^n$ whose support is contained in a tubular neighborhood of an algebraic subvariety. We also give a sufficient condition guaranteeing that a negative psh current is Liouville. Moreover, we prove that every negative psh algebraic current is Liouville. For the particular case of closed currents, under adequate support conditions, we obtain a structure theorem.},
affiliation = {Département de Mathématique, Faculté des sciences de Monastir, 5000 Monastir Tunisie.; Département de Mathématique, Faculté des sciences de Monastir, 5000 Monastir Tunisie.},
author = {Elkhadhra, Fredj, Mimouni, Souad},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {plurisubharmonic currents; Liouville currents; negative psh current; algebraic current; closed currents},
language = {eng},
number = {3-4},
pages = {651-674},
publisher = {Université Paul Sabatier, Toulouse},
title = {A Liouville theorem for plurisubharmonic currents},
url = {http://eudml.org/doc/115872},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Elkhadhra, Fredj
AU - Mimouni, Souad
TI - A Liouville theorem for plurisubharmonic currents
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2010
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - 3-4
SP - 651
EP - 674
AB - The goal of this paper is to extend the concepts of algebraic and Liouville currents, previously defined for positive closed currents by M. Blel, S. Mimouni and G. Raby, to psh currents on ${\mathbb{C}}^n$. Thus, we study the growth of the projective mass of positive currents on ${\mathbb{C}}^n$ whose support is contained in a tubular neighborhood of an algebraic subvariety. We also give a sufficient condition guaranteeing that a negative psh current is Liouville. Moreover, we prove that every negative psh algebraic current is Liouville. For the particular case of closed currents, under adequate support conditions, we obtain a structure theorem.
LA - eng
KW - plurisubharmonic currents; Liouville currents; negative psh current; algebraic current; closed currents
UR - http://eudml.org/doc/115872
ER -

References

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