Limit currents and value distribution of holomorphic mappings

Daniel M. Burns, Jr. (Ann Arbor)

We discuss the existence of d-closed or $dd^c$-closed positive currents associated to a holomorphic map $\phi$ as cluster points of normalized, weighted truncated image currents. The existence of such currents is controlled by higher dimensional analogues of the Ahlfors length-area inequalities, and such currents are sometimes called Ahlfors currents.

The method is very flexible through the choice of a weighting function. We give some applications to problems in value distribution theory. This is joint work with Nessim Sibony.