Asymptotic tracts of locally univalent functions

Barth, Karl F. and Rippon, Philip J. (2002). Asymptotic tracts of locally univalent functions. Bulletin of the London Mathematical Society, 34 pp. 200–204.

DOI: https://doi.org/10.1112/s0024609301008815

Abstract

Several results are proved which are related to an old problem of G.R. MacLane, namely, whether functions in the class $\mathcal{A}$ that are locally univalent can have arc tracts. In particular, a proof is given of an assertion of MacLane that if $f\in\mathcal{A}$ is locally univalent and has no arc tracts, then $f'\in\mathcal{A}$.

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