On Minimally Thin Sets in a Stolz Domain
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 219-223
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Let D denote the open right half plane and a Stolz domain in D with vertex at the origin. If h is a minimal harmonic function on D with pole at the origin then E⊂D is minimally thin at the origin iff where is the reduced function of h on E in the sense of Brelot. We now define where s shall be fixed to be 1/e. For the set E∩In we shall let cn denote the outer ordinary capacity (see [1, pp. 320-321]), An the outer logarithmic capacity, and on the outer Green capacity with respect to D. If E⊂K, Mme. Lelong [3, p. 131] was able to prove that E is minimally thin at the origin Since one cannot easily relate the classical measure theoretic properties of a plane set with its Green capacity, it would appear desirable to find some other criteria for minimal thinness.
Jackson, H. L. On Minimally Thin Sets in a Stolz Domain. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 219-223. doi: 10.4153/CMB-1972-040-8
@article{10_4153_CMB_1972_040_8,
author = {Jackson, H. L.},
title = {On {Minimally} {Thin} {Sets} in a {Stolz} {Domain}},
journal = {Canadian mathematical bulletin},
pages = {219--223},
year = {1972},
volume = {15},
number = {2},
doi = {10.4153/CMB-1972-040-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-040-8/}
}
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