Limit currents and value distribution of holomorphic maps
Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 145-176.

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.

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 dans une variété Y. Nous donnons quelques applications à la théorie de distribution de valeurs.

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, Volume 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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