no. 1
Limit currents and value distribution of holomorphic maps
[Courants limites et distribution de valeurs des applications holomorphes]
Burns, Daniel1 ; Sibony, Nessim2
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, Tome 62 (2012) no. 1, pp. 145-176.

Nous introduisons des courants positifs d-fermés ou dd c -fermés associés à une application holomorphe φ entre deux variétés complexes. Les courants sont de bidegré (p,p) selon les indicateurs de croissance de φ. Ce sont les analogues des courants d’Ahfors associés aux applications de ℂ dans une variété Y. Nous donnons quelques applications à la théorie de distribution de valeurs.

We construct d-closed and dd 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.

DOI : 10.5802/aif.2703
Classification : 32A22, 32H25, 32H30
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

Burns, Daniel 1 ; Sibony, Nessim 2

1 University of Michigan Department of Mathematics Ann Arbor MI 48109 (USA)
2 Université Paris-Sud Département Mathématiques UMR 8628 91405 Orsay (France) 
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Burns, Daniel; Sibony, Nessim. Limit currents and value distribution of holomorphic maps. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 145-176. doi : 10.5802/aif.2703. https://aif.centre-mersenne.org/articles/10.5802/aif.2703/

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