Value distribution and potential theory

Details Value distribution and potential theory Value distribution and potential theory

2003-04-22

arxiv.org/abs/math/0304332v1

Proceedings of the ICM, Beijing 2002, vol. 2, 681--690

Mathematics

Complex Variables

Scientific paper

We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between Riemannian manifolds, a version of the Second Main Theorem of Nevanlinna for curves in projective space and non-linear divisors, description of extremal functions in Nevanlinna theory and results related to Cartan's 1928 conjecture on holomorphic curves in the unit disc omitting hyperplanes.

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