On a problem of MacLane concerning arc tracts

Barth, Karl F. and Rippon, Philip J. (2004). On a problem of MacLane concerning arc tracts. Computational Methods and Function Theory, 4 pp. 405–418.

URL: http://www.heldermann.de/CMF/CMF04/CMF042/cmf0427....

Abstract

G.R. MacLane posed the question of whether a locally univalent function in the MacLane class ${\mathcal A}$ can have an arc tract. We show that the behaviour of any such example must be extremely irregular. We also indicate one possible approach to constructing an example of such a function, which relates MacLane's question to the `type problem' for certain Riemann surfaces.

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