Limit currents and value distribution of holomorphic maps

Daniel Burns[1]; Nessim Sibony[2]

  • [1] University of Michigan Department of Mathematics Ann Arbor MI 48109 (USA)
  • [2] Université Paris-Sud Département Mathématiques UMR 8628 91405 Orsay (France)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 145-176
  • ISSN: 0373-0956

Abstract

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We construct d -closed and d d c -closed positive currents associated to a holomorphic map φ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.

How to cite

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Burns, Daniel, and Sibony, Nessim. "Limit currents and value distribution of holomorphic maps." Annales de l’institut Fourier 62.1 (2012): 145-176. <http://eudml.org/doc/251089>.

@article{Burns2012,
abstract = {We construct $d$-closed and $dd^c$-closed positive currents associated to a holomorphic map $\phi $ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.},
affiliation = {University of Michigan Department of Mathematics Ann Arbor MI 48109 (USA); Université Paris-Sud Département Mathématiques UMR 8628 91405 Orsay (France)},
author = {Burns, Daniel, Sibony, Nessim},
journal = {Annales de l’institut Fourier},
keywords = {Ahlfors currents; Brody’s theorem; value distribution theory; equidistribution; Brody's theorem},
language = {eng},
number = {1},
pages = {145-176},
publisher = {Association des Annales de l’institut Fourier},
title = {Limit currents and value distribution of holomorphic maps},
url = {http://eudml.org/doc/251089},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Burns, Daniel
AU - Sibony, Nessim
TI - Limit currents and value distribution of holomorphic maps
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 145
EP - 176
AB - We construct $d$-closed and $dd^c$-closed positive currents associated to a holomorphic map $\phi $ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.
LA - eng
KW - Ahlfors currents; Brody’s theorem; value distribution theory; equidistribution; Brody's theorem
UR - http://eudml.org/doc/251089
ER -

References

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