Asymptotic values of strongly normal functions

Barth, Karl F. and Rippon, Philip J. (2005). Asymptotic values of strongly normal functions. Arkiv för Matematik, 43(1) pp. 69–84.

DOI: https://doi.org/10.1007/BF02383611

URL: http://link.springer.com/article/10.1007/BF0238361...

Abstract

Let f be meromorphic in the open unit disc D and strongly normal; that is,

(1 - |z|2) f# (z) → 0as|z| → 1,

where f# denotes the spherical derivative of f. We prove results about the existence of asymptotic values of f at points of C ∂D. For example, f has asymptotic values at an uncountably dense subset of C, and the asymptotic values of f form a set of positive linear measure.

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