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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.

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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.

Item Type: Journal Article
ISSN: 1617-9447
Keywords: MacLane class; locally univalent; arc tract; type problem; Asymptotic tract; Koebe arcs; Riemann surface
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3654
Depositing User: Philip Rippon
Date Deposited: 29 Jun 2006
Last Modified: 02 Dec 2010 19:50
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