We construct -closed and -closed positive currents associated to a holomorphic map 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.
Nous introduisons des courants positifs -fermés ou -fermés associés à une application holomorphe entre deux variétés complexes. Les courants sont de bidegré selon les indicateurs de croissance de . Ce sont les analogues des courants d’Ahfors associés aux applications de dans une variété . Nous donnons quelques applications à la théorie de distribution de valeurs.
Keywords: Ahlfors currents, Brody’s theorem, value distribution theory, equidistribution
Mot clés : Courants d’Ahlfors, théorème de Brody, théorie de la distribution de valeurs, équidistribution
@article{AIF_2012__62_1_145_0, author = {Burns, Daniel and Sibony, Nessim}, title = {Limit currents and value distribution of holomorphic maps}, journal = {Annales de l'Institut Fourier}, pages = {145--176}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {1}, year = {2012}, doi = {10.5802/aif.2703}, zbl = {1252.32002}, mrnumber = {2986269}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2703/} }
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 SP - 145 EP - 176 VL - 62 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2703/ DO - 10.5802/aif.2703 LA - en ID - AIF_2012__62_1_145_0 ER -
%0 Journal Article %A Burns, Daniel %A Sibony, Nessim %T Limit currents and value distribution of holomorphic maps %J Annales de l'Institut Fourier %D 2012 %P 145-176 %V 62 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2703/ %R 10.5802/aif.2703 %G en %F AIF_2012__62_1_145_0
Burns, Daniel; Sibony, Nessim. Limit currents and value distribution of holomorphic maps. Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 145-176. doi : 10.5802/aif.2703. http://www.numdam.org/articles/10.5802/aif.2703/
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