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Limit currents and value distribution of holomorphic maps

Daniel BurnsNessim Sibony — 2012

Annales de l’institut Fourier

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.

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