Limit currents and value distribution of holomorphic maps  [ Courants limites et distribution de valeurs des applications holomorphes ]
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 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.

Reçu le : 2010-06-10
Accepté le : 2010-10-05
DOI : https://doi.org/10.5802/aif.2703
Classification : 32A22,  32H25,  32H30
Mots 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'institut Fourier},
     volume = {62},
     number = {1},
     year = {2012},
     doi = {10.5802/aif.2703},
     zbl = {1252.32002},
     mrnumber = {2986269},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2012__62_1_145_0/}
}
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/item/AIF_2012__62_1_145_0/

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