Limit currents and value distribution of holomorphic maps

Details Limit currents and value distribution of holomorphic maps Limit currents and value distribution of holomorphic maps

2010-05-24

arxiv.org/abs/1005.4330v2

Mathematics

Complex Variables

Revised, June 10, 2010: typos corrected

Scientific paper

We construct $d$-closed and $dd^c$-closed positive currents associated to a holomorphic map $\phi$ 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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