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.
Research supported in part by a grant from NSA
Research supported in part by a grant from NSERC
"Martin boundaries of sectorial domains." Ark. Mat. 31 (1) 27 - 49, March 1993. https://doi.org/10.1007/BF02559496