A nullset for normal functions in several variables

Juhani Riihentaus
1990 Proceedings of the American Mathematical Society  
Suppose that Q is a domain in Cn , E c Q. is closed in Í2, and /: Q\E -► C* is a meromorphic function. We show that if / is normal and E is an analytic subvariety or, more generally, of locally finite (2n -2)dimensional Hausdorff measure in £2 satisfying a certain geometric condition, then / can be extended to a meromorphic function (= holomorphic mapping) / * : £2 -> C* . In the case of a subvariety sufficient, but not necessary, for the geometric condition is that the singularities of E are
more » ... larities of E are normal crossings. As a digression, we give a new proof for the following result, due to Parreau in the case n = 1 : if / is in the Nevanlinna class and E is polar (in R "), then f has a meromorphic extension f to £2.
doi:10.1090/s0002-9939-1990-1028048-0 fatcat:p5kzwap2pne75nx2txjtybja2u