Limit currents and value distribution of holomorphic maps

Abstract

We construct $d$-closed and $d{d}^c$-closed positive currents associated to a holomorphic map $\varphi$ 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.

Revised, June 10, 2010: typos corrected