# 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.

## Abstract

G.R. MacLane posed the question of whether a locally univalent function in the MacLane class 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.