Courants algébriques et courants de Liouville

M. Blel; S. K. Mimouni; G. Raby

Annales Polonici Mathematici (2005)

  • Volume: 86, Issue: 3, page 245-271
  • ISSN: 0066-2216

Abstract

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We define in ℂⁿ the concepts of algebraic currents and Liouville currents, thus extending the concepts of algebraic complex subsets and Liouville subsets. After having shown that every algebraic current is Liouville, we characterize those positive closed currents on ℂⁿ which are algebraic. Let T be a closed positive current on ℂⁿ. We give sufficient conditions, relating to the growth of the projective mass of T, so that T is Liouville. These results generalize those previously obtained by N. Sibony and P. M. Wong, and K. Takegoshi in the geometrical case, i.e. when T=[X] is the current of integration on an analytical complex subset of ℂⁿ.

How to cite

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M. Blel, S. K. Mimouni, and G. Raby. "Courants algébriques et courants de Liouville." Annales Polonici Mathematici 86.3 (2005): 245-271. <http://eudml.org/doc/281044>.

@article{M2005,
author = {M. Blel, S. K. Mimouni, G. Raby},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic function; positive current; complex analytic set; algebraic set; Liouville property},
language = {fre},
number = {3},
pages = {245-271},
title = {Courants algébriques et courants de Liouville},
url = {http://eudml.org/doc/281044},
volume = {86},
year = {2005},
}

TY - JOUR
AU - M. Blel
AU - S. K. Mimouni
AU - G. Raby
TI - Courants algébriques et courants de Liouville
JO - Annales Polonici Mathematici
PY - 2005
VL - 86
IS - 3
SP - 245
EP - 271
LA - fre
KW - plurisubharmonic function; positive current; complex analytic set; algebraic set; Liouville property
UR - http://eudml.org/doc/281044
ER -

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