Limit currents and value distribution of holomorphic maps

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 referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.

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