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March 1993 Martin boundaries of sectorial domains
Michael C. Cranston, Thomas S. Salisbury
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Ark. Mat. 31(1): 27-49 (March 1993). DOI: 10.1007/BF02559496

Abstract

LetD be a domain in R2 whose complement is contained in a pair of rays leaving the origin. That is, D contains two sectors whose base angles sum to 2π. We use balayage to give an integral test that determines if the origin splits into exactly two minimal Martin boundary points, one approached through each sector. This test is related to other integral tests due to Benedicks and Chevallier, the former in the special case of a Denjoy domain. We then generalise our test, replacing the pair of rays by an arbitrary number.

Funding Statement

Research supported in part by a grant from NSA
Research supported in part by a grant from NSERC

Citation

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Michael C. Cranston. Thomas S. Salisbury. "Martin boundaries of sectorial domains." Ark. Mat. 31 (1) 27 - 49, March 1993. https://doi.org/10.1007/BF02559496

Information

Received: 28 August 1991; Published: March 1993
First available in Project Euclid: 31 January 2017

zbMATH: 0841.31009
MathSciNet: MR1230263
Digital Object Identifier: 10.1007/BF02559496

Rights: 1993 © Institut Mittag-Leffler

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Vol.31 • No. 1 • March 1993
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