Computational Methods and Function Theory 4 (2004), No. 2, 405--418
Copyright Heldermann Verlag 2004
Karl F. Barth
kfbarth@mailbox.syr.edu , Department of Mathematics, Syracuse University, Syracuse, NY 13244, U.S.A.
Philip J. Rippon
p.j.rippon@open.ac.uk , Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, U.K.
G. R. MacLane posed the question of whether a locally univalent function in the MacLane class 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.
Keywords: Asymptotic tract, MacLane class, Koebe arcs, Riemann surface.
MSC 2000: Primary 30D40.
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